case study questions from coordinate geometry class 9

Class 9 Maths Case Study Questions Chapter 3 Coordinate Geometry

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Case study Questions in Class 9 Mathematics Chapter 3 are very important to solve for your exam. Class 9 Maths Chapter 3 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 9 Maths Case Study Questions Chapter 3 Coordinate Geometry

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In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 3 Coordinate Geometry

Case Study/Passage-Based Questions

case study questions from coordinate geometry class 9

Answer: (d) 2 units

(ii) How far is the library from Shaguns house?

Answer: (b) 2 units

(iii) How far is the library from Alia’s house?

Answer: (d) None of these

(iv) Which of the following is true?

Answer: (b) ABC forms an isosceles triangle

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of house from grocery store to that from electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to the food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

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Case Study Questions for Class 9 Maths Chapter 3 Coordinate Geometry

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Case Study Questions

Question 1:

Saumya has to reach her office every day at 10:00 am. On the way to her office, she drops her son at school. Now, the location of Saumya’s house, her son’s school and her office are represented by the map below. Using the details given, answer the following questions.

Q1. Find the coordinates of Saumya’s home. (a) (1, 4) (b) (4, 1) (c) (7, 1) (d) (1, 7)

Q2. Find the coordinates of Saumya’s office. (a) (7, 5) (b) (5, 7) (c) (7, 1) (d) (1, 7)

Q3. Find the coordinates of Saumya’s son’s school. (a) (1, 4) (b) (4, 1) (c) (7, 1) (d) (1, 7)

Q4. Find the distance between Saumya’s home and her son’s school. (a) 7km (b) 4km (c) 3km (d) 1km

Q5. Find the distance between Saumya’s office and her son’s school. (a) 7km (b) 4km (c) 3km (d) 1km

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CBSE Case Study Questions for Class 9 Maths Coordinate Geometry Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 9 Maths Coordinate Geometry in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

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CBSE Case Study Questions for Class 9 Maths Coordinate Geometry PDF

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Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023

Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023 Study Materials Sep-08 , 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Coordinate Geometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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Coordinate geometry case study questions with answer key.

Final Semester - June 2015

(b) What are the coordinates of C and D respectively?

(d) What is the distance between A and C?

(e) What are the coordinates of the point of intersection of AC and BD?

(ii) What are the coordinates of Police Station?

(iii) Distance between school and police station:

(iv) What are the coordinates of Library?

(v) In which quadrant the point (-1, 4) lies?

(b) What are the coordinates of A and B respectively?

(d) The point on the y-axis ( in sketch 2) which is equidistant from the points B and C is

(e) The point on the x-axis ( in sketch 2) which is equidistant from the points C and D is

(b) What are the coordinates of R, taking A as origin?

(d) Shape of lawn is :

(e) Area of lawn is :

(ii) What are the coordinates of position 'D'?

(iii) What are the coordinates of position 'H'?

(iv) In which quadrant, the point 'C' lie?

(v) Find the perpendicular distance of the point E from the y-axis.

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Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry

Download Important Questions for Class 9 Maths Chapter 3 - Coordinate Geometry - Free PDF

Welcome to our comprehensive collection of Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry available in Vedantu. As students progress through their academic journey, mastering the concepts of Coordinate Geometry becomes essential. Our carefully curated list of questions aims to provide students with a thorough understanding of this chapter and boost their problem-solving skills. With a focus on CBSE guidelines and exam patterns, these questions cover various topics such as plotting points, finding distances, and calculating gradients on the coordinate plane. Whether you're looking to strengthen your knowledge or preparing for exams, our curated set of important questions is a valuable resource to excel in Coordinate Geometry. Get ready to explore the fascinating world of coordinates and elevate your mathematical prowess!

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Also, check CBSE Class 9 Maths Important Questions for other chapters:

Study Important Questions for Class - 9 Mathematics Chapter – 3 Coordinate Geometry

Section - A

1 On which axes do the given points lie?

ii. (0, -3)

iii. (0, 6)

iv. (-5, 0)

i. (7,0) X-axis since the y component is zero

ii. (0, -3) Y-axis since the x component is zero

iii. (0,6) Y-axis since the x component is zero

iv. (-5,0) X-axis since the y component is zero

2 In which quadrants do the given points lie?

ii. (-3, 7)

iii. (-1, -2)

iv. (3, 6)

i. (4,-2) IV quadrant since the x component is positive and y component is negative

ii. (-3,7) II quadrant since the x component is negative and y component is positive

iii. (-1,-2) III quadrant since the x component is negative and y component is negative

iv. (3,6) I quadrant. since the x component is positive and y component is positive

3. Do P (3, 2) & Q(2, 3) represent the same point?

Ans: P(3,2) and Q(2,3) do not represent the same point. The first one has the x component is 3 and y is two, while Q has the x component as 2 and y component is 3.

4. In which quadrant points P(3,0), Q(6,0) , R (-7.0), S (0,-6), lie?

Ans: These points do not lie in any quadrant. These points lie on the axes.

5. If a<0 and b<0, then the point P(a,b) lies in

a) quadrant IV

b) quadrant II

c) quadrant III

d) quadrant I

Ans: (c) quadrant III

6. The points (other than the origin) for which the abscissa is equal to the ordinate lie in

a) Quadrant I only

b) Quadrant I and II

c) Quadrant I & III

d) Quadrant II only.

Ans: (c) quadrant I & III.

In III and I quadrants, the axes have the same sign.

7. The perpendicular distance of the point P(4,3) from the y axis is

c) 7 Units

Ans: (a) 3 units

Distance from the Y axis is the x coordinate of the point.

8. The area of triangle OAB with 0(0,0), A(4,0) & B(0,6) is

a) 8 sq. unit

b) 12 sq. units

c) 16 sq. units

d) 24 sq. units

Ans: (b) 12 sq. units.

Area is half of the product of base and height of the triangle.

Section - B

9. Write down the coordinates of each of the points P, Q, R, S and T as shown in the following figure?

10. Draw the lines X'OX and YOY as the axes on the plane of a paper and plot the given points.

ii. B (-3, 2)

iii. C(-5, -4)

iv. D(2,-6)

Section - C

11. Find the mirror images of the following point using x-axis & y-axis as mirror.

ii. B(2,-3)

iii. C(-2,3)

iv. D(-2,-3)

Ans:

i. A’ (2,-3),

ii. B’ (2,3)

iii. C’ (-2,-3),

iv. D’ (-2,3)

12. Draw the graph of the following equations

i. \[{\bf{y}} = {\bf{3x}} + {\bf{2}}\]

ii. \[{\bf{y}} = {\bf{x}}\]

${\bf{y}} = {\bf{x}}$

13. Draw a triangle with vertices 0(0,0) A(3,0) B(3,4). Classify the triangle and also find its area.

Ans: The points from a right angle triangle

The area of the triangle is half of the product of the base and height i.e. 6 square units.

14. Draw a quadrilateral with vertices A(2,2) B(2,-2) C(-2,-2), D(-2,2). Classify the quadrilateral and also find its area.

This quadrilateral is square of area =16 square units.

15. Find the coordinates of point which are equidistant from these two points P(3,0) and Q(-3,0). How many points are possible satisfying this condition?

Ans: All the point on the Y-axis satisfy this condition.

1 Mark Questions

1. The point of intersection of X and Y axes is called

(a) zero point

(d) none of these

Ans: (b) origin

2. The distance of the point (-3, -2) from x-axis is

(a) 2 units

(b) 3 units

(d) 13 units

Ans: (a) 2 units

Distance from the x axis is the magnitude/absolute value of the y coordinate of the point.

3. The distance of the point (-6, -2) from y-axis is

(a) 6 units

(b) 10 units

(d) 8 units

Ans : (a) 6 units

Distance from the y axis is the magnitude/absolute value of the x coordinate of the point.

4. The abscissa and ordinate of the point with Co-ordinates (8, 12) is

(a) abscissa 12 and ordinate 8

(b) abscissa 8 and ordinate 12

(d) none of these

Ans: (a) abscissa 12 and ordinate 8

Abscissa is the y coordinate of the point and the ordinate is the x coordinate value.

5. The co-ordinate of origin in

(b) (0, y)

(d) none of these.

Ans : (c) (0, 0)

For the origin, both abscissa and ordinate are 0.

6. The distance of the point (2,3) from y axis’s

(A) 2 units

(B) 3 units

(D) 13 units

Ans: (A) 2 units

Distance from the x axis is the magnitude/absolute value of the y coordinate of the point. And the distance from the y axis is the magnitude/absolute value of the x coordinate of the point.

7. The point (-2, -1) lies in

(A) 1st quadrant

(B) 2nd quadrant

(D) 4th quadrant

Ans: (C) 3rd quadrant

3 rd quadrant corresponds to both negative x and y values.

8. The point (3,0) lies on

(A) +ve x axis

(B) – ve x axis

(D) –ve y axis

Ans: (A) +ve x axis

Since the y coordinate is zero and x-coordinate is positive.

9. The distance of the point (3, 5) from x- axis is

(a) 3 units

(b) 4 units

(d) 6 units

Ans: (c) 5 units

10. The point (0, -5) lies on

(a) +ve x- axis

(b) +ve y- axis

(d) –ve y-axis

Ans: (d) –ve y-axis

Since the x-coordinate is zero and y is negative.

11. The point (-2, 5) lies in

(a) 1st quadrant

(b) 2nd quadrant

(d) 4th quadrant

Ans: (b) 2nd quadrant.

In the second quadrant, the x-values are negative and y are positive.

12. The distance of the point (3, 0) from x- axis is

(b) 0 units

Ans: (a) 3 units.

2 Marks Questions

1. Write the name of each part of the plane formed by Vertical and horizontal lines.

Ans: Vertical line is called y-axis, the horizontal line is called x-axis. And these form four quadrants.

2. Write the Co-ordinates of a point which lies on the x-axis and is at a distance of 4units to the right of origin. Draw its graph.

Ans: (4, 0)

3. Write the mirror image of the point (2, 3) and (-4, -6) with respect to x-axis.

Ans: The mirror image of point (2, 3) is (2, -3) with respect to x-axis.

The mirror image of (-4, -6) is (-4,6) with respect to the x-axis.

4. Write the Coordinates of a point which lies on the y-axis and is at a distance of 3 units above x-axis. Represent on the graph.

Ans: The Coordinates of the point which lies on y-axis and at a distance of 3units above x- axis is (0, 3).

5. Write abscissa and ordinate of point (-3, -4)

Ans: Abscissa -3 ordinate -4

6. State the quadrant in which each of the following points lie:

(ii) (-7,11)

(iii) (-6, -4)

(iv) (-5, -5)

Ans: (2, 1) I Quadrant

(-7, 11) II Quadrant

(-6, -4) III Quadrant

(-5, -5) III Quadrant

7. Which of the following points belongs to 2nd quadrant

(ii) (-3,2)

(iii) (2,0)

(iv) (-4,2)

Ans: The points (-3, 2), (-4, 2) belong to the 2nd quadrant.

8. What is the name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans: The horizontal line is called x –axis and the name of vertical line is y – axis

9. Name the points of the plane which do not belong to any of the quadrants.

Ans: The points in a plane which do not belong to any one of the quadrants is origin which is denoted by O (0,0).

10. Which of the following points belong to the x- axis?

(a) (2, 0) (b) (3, 3) (c) (0, 1) (d) (-2, 0)

Ans: (2, 0) and (-2, 0) belong to the x- axis.

To belong on the y axis the y-component should be zero.

11. Which of the following points belongs to 1st quadrant

(a) (3, 0) (b) (1, 2) (c) (-3, 4) (d) (3, 4)

Ans: (1, 2) and (3, 4) belong to the 1st quadrant.

12. Which of the following points belongs to 3rd quadrant

(a) (1, 3) (b) (-1, -3) (c) (0, 4) (d) (-4, -2)

Ans: (-1, -3) and (-4, -2) belong to the 3rd quadrant.

3 Marks Questions

1. How will you describe the position of a table lamp on your study table to another person?

Consider the figure of a tabletop, on which a lamp (L) is placed.

Consider the lamp on the table as a point and the table as a plane.

Choose one of the corners as the Origin-O (0,0). Measure the distance of the lamp from the shorter edge and the longer edge. Let us assume that the distance of the lamp from the shorter edge is 3m and from the longer edge, its 2m.

Therefore, we can conclude that the position of the lamp on the table can be described in two ways depending on the order of the axes as (3,2).

2. Write the answer of each of the following questions:

(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans: The horizontal line that is drawn to determine the position of any point in the Cartesian plane is named the x-axis and the vertical line is called the y-axis.

(ii) What is the name of each part of the plane formed by these two lines?

Ans: The name of each part of the plane that is formed by x-axis and y-axis is called a quadrant.

(iii) Write the name of the point where these two lines intersect.

Ans: The point, where the x-axis and the y-axis intersect is called the origin denoted by O(0,0).

3. In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (-1,0), (1,2) and (–3,–5) lie? Verify your answer by locating them on the Cartesian plane.

Ans: Tpoint (– 2, 4) lies in II quadrant;

the point (3, – 1) lies in IV quadrant;

the point (– 2, 4) lies in II quadrant;

the point (3, – 1) lies in IV quadrant and

the point (–1, 0) lies on the x-axis.

These can be verified from the figure below.

4. Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

5. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (-3, 5), (-3, -5) and (6, 1) in the Cartesian plane.

6. Take a triangle ABC with A (3, 0), B (-2, 1), C (2, 1). Find its mirror image.

Ans: Mirror images of A (3, 0), B (-2, 1) and C (2, 1) about the x-axis are A’ (3, 0), B’(-2,-1), C’(2,-1) respectively.

7. In fig. write the Co-ordinates of the points and if we join the points write the name of fig. formed. Also write Co-ordinate of intersection point of AC and BD.

(i) The Co-ordinate of point A is (0, 2), B is (2, 0), C is (0, -2) and D is (-2,0).

(ii) It we joined them we get square.

(iii) Co-ordinate of intersection point of AC and BD is (0, 0).

8. In which quadrant or on which axis do each of the points (-2, 4), (2, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane.

(-2, 4) lies in II quadrant;

(2, -1) lies in IV quadrant;

(-1, 0) lies on –ve x-axis;

(1, 2) lies in I quadrant and

(-3, -5) lies in III quadrant.

This can be verified using the following graph:

9. In fig of vertices find co-ordinates of triangle ABC

Ans: (A) (0, 0) (B) (2, 3) (c) (-2, 3)

10. Take a quadrilateral ABCD

(A) (-5, -4) (B) (-5, 2) (C) (-3, 3) and (D) (-3, 4) find its mirror image with respect to y- axis.

Ans: The mirror image of point.

(A) (-5, 4) (B) (-5, 2) (C) (-3, 3) and (D) (-3, 4) wrt y-axis are.

A’ (5, 4), B’ (5, 2), C’ (3, 3) and D’ (3, 4)

11. Locate the points (A) (-3, 4) (B) (3, 4) and (C) (0, 0) in a Cartesian plane write the name of figure which is formed by joining them.

The figure formed is a triangle.

12. Find Co-ordinates of vertices of rectangle ABCD

Ans: The co- ordinates of vertices of rectangle A (2, 2), B (-2, 2), C (-2, -2) and D (2, -2).

13. Take a rectangle ABCD with A (-6, 4), B (-6, 2), C (-2, 2) and D (-2, 4). Find its mirror image with respect to x- axis.

Ans: The mirror image of A (-6, 4) is A’ (-6, -4) and B (-6, 2) is B’ (-6, -2), C (-2, 2) is C’ (-2, -2) and D (-2, 4) is D’ (-2, -4)

14. The following table gives measures (in degrees) of two acute angles of a right triangle

Plot the point and join them.

Measures of two acute angles of a right triangle

15. Plot each of the following points in the Cartesian Plane

(b) (-3, -4)

(d) (2, -5)

(e) (2, 0)

4 Marks Questions

1. (Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East – West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

(i) how many cross - streets can be referred to as (4, 3).

(ii) how many cross - streets can be referred to as (3, 4).

Ans: We need to draw two perpendicular lines as the two main roads of the city that cross each other at the center and let us mark it as N-S and E-W.

Let us take the scale as 1 cm = 200m.

Following figure shows the perpendicular roads .

(i) From the figure it can be inferred that only one point have the coordinates as (4,3). Hence, it can be concluded that only one cross - street can be referred to as (4, 3).

(ii) Only one point have the coordinates as (3,4). Therefore, it can be concluded that only one cross - street can be referred to as (3, 4).

2. See Fig.3.14, and write the following:

(i) The coordinates of B.

Ans: The coordinates of point B in the above figure is the distance of point B from x-axis and y- axis. Therefore, we can conclude that the coordinates of point B are (―5, 2).

(ii) The coordinates of C.

Ans: The coordinates of point C in the above figure is the distance of point C from x-axis and y- axis. Therefore, we can conclude that the coordinates of point C are (5, ―5).

(iii) The point identified by the coordinates (–3, –5).

Ans: The point E represents the coordinates (―3, ―5).

(iv) The point identified by the coordinates (2, – 4).

Ans: The point G that represents the coordinates (2, ―4).

(v) The abscissa of the point D.

Ans: The abscissa of point D in the given figure is the distance of point D from the y-axis which is 6.

(vi) The ordinate of the point H.

Ans: The ordinate of point H in the above figure is the distance of point H from the x-axis which is ―3.

(vii) The coordinates of the point L.

Ans: The coordinates of point L in the above figure is the distance of point L from x-axis and y-axis. Therefore, we can conclude that the coordinates of point L are (0, 5).

(viii) The coordinates of the point M.

Ans: The coordinates of point M in the above figure is the distance of point M from x-axis and y-axis. Therefore, we can conclude that the coordinates of point M are (―3, 0).

5 Marks Questions

1. See fig. and write the following

(i) The Co-ordinates of B

Ans: (-5,2)

(ii) The Co-ordinates of C

Ans: (5, -5)

(iii) On which axis point L lies.

Ans: Y-axis

(iv) The abscissa of the point D

Ans: As shown in the figure the abscissa of point D is 6.

(v) The Co-ordinates of point L

Ans: (0, 5)

(vi) On which axis point M lies.

Ans: Point M lies on X-axis.

(vii) The ordinate of the point H

Ans: The ordinate of point H is -3

(viii) The Co-ordinates of the point M

Ans: (-3, 0)

(ix) The point identified by the Co-ordinate (2, -4)

Ans: G has the coordinate (2,-4)

(x) The point identified by the Co-ordinates (-3, -5)

Ans: E has the coordinate (-3,-5)

2. Find some ordered pairs of the linear equation \[{\bf{2x}} + {\bf{y}} = {\bf{4}}\] and plot them ‘how many such ordered pairs can be found and plotted?

Ans: The given equation is \[2x + y = 4\] The equation holds if

\[x = 0,\,y = 4\] i.e. (0, 4),

\[x = 1,\,y = 2\] i.e. (1, 2),

\[x = 2,\,y = 0\] i.e. (2, 0) ,

\[x = 3,\,y = - 2\] i.e. (3, -2)…

Similarly (4,-4), (5,-6), (-1,6), (-2,8) etc. also. These are a few ordered pares which are valid solutions. And there are infinite such ordered pairs

3. The following table given the relation between natural numbers and odd natural numbers

Plot the points and join them. Do you get a straight line by joining these points?

Straight line is obtained by joining Points

Yes a straight line is obtained by joining these points.

Chapter 3 Maths Class 9 Important Questions - Free PDF Download

The Coordinate Geometry Class 9 Important Questions present reliable and accurate learning elements for students to understand the chapter efficiently. The students will receive the necessary understanding of the chapters to clear the difficult problems in class. Expert subject teachers of mathematics prepare these questions. Hence, solving these questions will help students obtain a better understanding of the type of questions asked in the examinations and how to format their answers correctly.

Vedantu presents a free PDF to download for Class 9 Chapter 3 Important Questions so that students can prepare well according to the CBSE syllabus. Students need to understand these guidelines and find solutions with a proper explanation. This free PDF online will surely help students understand their concepts and build a solid base on Coordinate Geometry.

Important Questions for Class 9 Maths Coordinate Geometry

Coordinate geometry is an intriguing subject where students get to learn about the object’s position in a plane, learn about the concepts and coordinates of the cartesian plane and so on. The topics covered in the chapter are :

Introduction

Cartesian System

Plotting a Point

Coordinate geometry.

Coordinate geometry deals with the locating points on a plane when the aligned numbers, called coordinates for a particular point, are given. It presents geometric aspects in Algebra and allows them to solve geometric problems.

Concepts of Coordinates

The intersection point of the x-axis and the y-axis is identified as the origin. Both x and y are 0 at this point.

The right-hand side of the x-axis values are positive, and the x-axis values on the left-hand side are negative.

Similarly, the values located above the origin on the y-axis, are positive, and the values are negative, which are located below the origin.

It is determined by a collection of two numbers, to locate a point on the plane.

Cartesian System

A Cartesian coordinate system is a system in two dimensions that can be used to locate a point with the help of two unique numbers called coordinates. The point along the x-axis is called the x-coordinate and the point along the y-axis is called the y-coordinate.

Two perpendicular directed lines are stipulated to define the coordinates, and the unit length is marked off on the two axes (fig 1). Cartesian coordinate systems are also used in higher space dimensions.

By using the Cartesian coordinate system, geometric shapes are represented by algebraic equations. For example, radius 2 circle may be defined by the equation x² + y² = 4 (Figure 2).

Distance Between Two Points

Distance between two points of the plane

(x₁, y₁) and (x₂, y₂) is d = [(x₂ – x₁)² + (y₂ – y₁)]¹/²

In case of a three-dimensional system, the formula of the distance between the points

(x₁, y₁, z₁) and (x₂, y₂, z₂) is d = [(x₂ – x₁)² + (y₂ – y₁)² + (z₂ – z₁)² ] 1/2

Vector Representation

The two-dimensions vector, from the origin to the point with the cartesian coordinates (x, y) can be written as r = xi + yj where i = (1,0) and j = (0,1) are vectors units in the direction of the x-axis and y-axis respectively.

In three-dimensions cases, we will have r = xi + yj + zk, where k = (0,0,1) is the vector unit in the direction of z-axis.

To plot or graph points, we can employ two perpendicular lines called the x-axis and the y-axes. The x-axis is horizontal, and the y axis is the vertical line. The part of the x-axis towards the right of origin is the positive x-axis, and the one towards the left of the origin is the negative x-axis. Similarly, the part of the y-axis above the origin is the positive y-axis, and the part of y-axis below the origin is the negative y-axis. In the coordinate plane, every point is designed by an assigned pair of x and y coordinates.

Let's Consider the Example

Using the Pencil, Plot the Point −4,3

The first coordinates inform about the right or left movement from the origin. The second coordinate tells about the up or down movement from the origin.

Since x coordinate is a −4, there is a movement towards the left 4 units from the origin. The coordinate of y is 3, which means movement two units vertically up to get to the point −4,3.

List of Important Questions for Class 9 Maths Chapter 3

Chapter 3 Maths Class 9 Important Questions include different types of questions that cover all the sub-topics of the entire chapter. Important questions from each topic are covered in the PDF to provide students with a clear and logical understanding of the chapter. Some of the important questions that are frequently asked in the exam from this chapter are-

In which axis or quadrant do each of the points (–2, 4), (3, –1), (–1, 0),(1, 2) and (–3, –5) lie? Prove your answer by placing them on the Cartesian plane.

Plot the points (y, z) in the following table on the plane, picking proper units of distance on the axes where

State the name of the point where two lines intersect.

Define the three-dimensional Cartesian coordinate system.

Locate the points in the Cartesian plane (0, 5), (5, 0), (2, 5), (–3, 5), (5, 2),(–3, –5), (5, –3) and (6, 1).

State the name of vertical lines and the horizontal lines formed to determine the position of any point in the Cartesian plane?

State the name of every part of the plane developed by two lines?

Describe the Cartesian plane.

Two rolling dice are rolled at the same time. Let the numbers on Dice1 and Dice 2 be denoted by y and z respectively. After each roll, the point S(y, z) is outlined in the plane. Plot all the probable positions of S, and highlight those positions for which the sum of y and z is 8.

In the Cartesian plane plot the five points for which ordinate and the abscissa are equal.

In the Cartesian plane plot the following points - A (1.3, 2.4), B ( - 2.7, 3.2), C ( - 1.1, - 3.6) and D (4, - 2)

Practice Questions from Class 9 Chapter 3 Maths Coordinate Geometry

1. Find the distance of the point (-3, 4) from the x-axis.

2. If the points A(x, 2), B(-3, 4) and C(7, -5) are collinear, then find the value of x.

3. For what value of k will k + 9, 2k – 1 and 2k + 7 be the consecutive terms of an A.P.?

4. Find the relation between x and y if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.

5. Find the ratio in which the y-axis divides the line segment joining the points A(5, -6) and B(-1, -4). Also, find the coordinates of the point of division.

6. Let P and Q be the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4) such that P is nearer to A. Find the coordinates of P.

Benefits of Chapter 3 Maths Class 9 Important Questions

The Basic Concepts of Coordinate Geometry assists students in achieving a high grade by providing a thorough comprehension of the chapter's principles. Pupils that understand the ideas, theories, and calculations can achieve higher percentages on their exams. The following are some of the advantages of significant problems for class 9 mathematics coordinate geometry:

The Coordinate Geometry Class 9 Important Questions PDF is prepared according to the examination guidelines to help students score well in the examinations.

Expert Mathematics subject teachers prepare these questions.

The questions are prepared after a thorough analysis of the previous year's question papers combining the syllabus’s revisions.

The PDF also comprises solutions so that students can refer to them in case of any doubts.

Students can check information about the topics by following the reference books or by searching them on the Vedantu portal.

Practising questions from the PDF will develop the student’s understanding of the concepts and the examination pattern.

Key Features of Important Questions Class 9 Maths Chapter 3 - Coordinate Geometry

All the questions are written from an examination point of view.

Step-by-step solutions for questions with accurate explanations.

The solutions are clear and easy to understand.

Learning is quick as they are clearly written by subject experts to match the curriculum.

These important questions help in developing a good conceptual foundation for students.

These solutions are absolutely free and available in PDF format.

Conclusion

Crucial Questions for Class 9 Mathematics Coordinate Geometry are essential and reputable sources of study material created for pupils in a well-structured and readily comprehensible style. It will assist pupils in properly comprehending the chapters. The pupils will get the understanding of the chapters required to solve the challenging issues in class. The crucial questions will assist students in covering all of the issues and scoring high marks.

FAQs on Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry

1. Which chapter is the most important in Class 9 Maths?

Chapter 3 of Class 9 Maths is about geometry which is the branch of Mathematics concerned with spatial connections among diverse things, individual object forms, and surrounding space characteristics. Class 9 is an important year for high school students since it is during this year that students lay the groundwork for all of the major topics and ideas covered in the Class 10 Board examinations. Students will learn how to identify points in a cartesian system or an XY plane in the chapter Coordinate Geometry. This notion is critical for determining the position of an object in a certain location.

2. How can I practise Chapter 3 of Class 9 Maths?

Geometry is the component of Mathematics that demands a comprehension of the topic as well as certain visualising abilities that students should work on to improve. Vedantu's Crucial Questions for Class 9 Mathematics Coordinate Geometry are valuable and trustworthy sources of study material supplied for students in a well-structured and easily understandable format. These vital questions are available for free on Vedantu (vedantu.com) and its mobile app. It will help pupils understand the chapters thoroughly. Students will get a grasp of the chapters needed to answer the difficult problems in class. The essential questions will help pupils cover all of the issues and achieve good grades.

3. What are case study questions in Class 9 Maths?

Case study questions in Class 9 Maths are the questions that introduce a particular scenario and its mathematical aspect and then proceeds to ask some questions that are relevant to the given chapter i.e. Coordinate Geometry in this case. Case study questions usually involve a real life-based situation where the questions check the students’ analytical ability to follow through and subsequently apply the Maths to it. They are extremely important as they carry a lot of marks and are really simple to get through.

4. How to plot a point?

To plot or graph points, we can use two perpendicular lines known as the x- and y-axes. The horizontal x-axis is parallel to the vertical y-axis. The positive x-axis is located to the right of the origin, while the negative x-axis is located to the left of the origin. Likewise, the positive y-axis is the part of the y-axis above the origin, and the negative y-axis is the part of the y-axis below the origin. Every point in the coordinate plane is defined by a given pair of x and y coordinates.

5. What is coordinate geometry?

Coordinate geometry is concerned with identifying points on a plane when the aligned values, known as coordinates for a certain point, are supplied. It introduces geometric concepts in Algebra and helps students to solve geometric problems. The origin is defined as the point at where the x-axis and y-axis connect. At this moment, both x and y are zero. To identify a point on the plane, a collection of two numbers is used.

CBSE Class 9 Maths Important Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak, Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

Now he told Raju to draw another line CD as in the figure
The teacher told Ajay to mark ∠ AOD as 2z
Suraj was told to mark ∠ AOC as 4y
Clive Made and angle ∠ COE = 60°
Peter marked ∠ BOE and ∠ BOD as y and x respectively

Now answer the following questions:

2y + z = 90°
2y + z = 180°
4y + 2z = 120°
(a) 2y + z = 90°

Class 9 Mathematics Case study question 3

(a) 31.6 m²
(c) 513.3 m³
(b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

Mycbseguide: blessing in disguise.

Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

MATHS PAAGAL HAI

All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

Where is search ? bar

maths is love

Can I have more questions without downloading the app.

I love math

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Unit 5: Coordinate Geometry

Coordinate plane.

Introduction to the coordinate plane (Opens a modal)
Points and quadrants example (Opens a modal)
Identify coordinates Get 3 of 4 questions to level up!
Identify points Get 5 of 7 questions to level up!
Cartesian plane nomenclature Get 3 of 4 questions to level up!
Quadrants on the coordinate plane Get 5 of 7 questions to level up!

Slope of a line

Intro to slope (Opens a modal)
Positive & negative slope (Opens a modal)
Worked example: slope from graph (Opens a modal)
Graphing a line given point and slope (Opens a modal)
Calculating slope from tables (Opens a modal)
Worked example: slope from two points (Opens a modal)
Slope review (Opens a modal)
Slope from graph Get 3 of 4 questions to level up!
Graphing from slope Get 3 of 4 questions to level up!
Slope in a table Get 3 of 4 questions to level up!
Slope from two points Get 3 of 4 questions to level up!

Horizontal and vertical lines

Slope of a horizontal line (Opens a modal)
Horizontal & vertical lines (Opens a modal)
Horizontal & vertical lines Get 5 of 7 questions to level up!

x-intercepts and y-intercepts

Intro to intercepts (Opens a modal)
x-intercept of a line (Opens a modal)
Intercepts from an equation (Opens a modal)
Intercepts from a table (Opens a modal)
Intercepts of lines review (x-intercepts and y-intercepts) (Opens a modal)
Intercepts from a graph Get 3 of 4 questions to level up!
Intercepts from an equation Get 3 of 4 questions to level up!
Intercepts from a table Get 3 of 4 questions to level up!

Applying intercepts and slope

Slope, x-intercept, y-intercept meaning in context (Opens a modal)
Slope and intercept meaning in context (Opens a modal)
Slope and intercept meaning from a table (Opens a modal)
Finding slope and intercepts from tables (Opens a modal)
Linear functions word problem: fuel (Opens a modal)
Using slope and intercepts in context Get 3 of 4 questions to level up!
Linear equations word problems: tables Get 3 of 4 questions to level up!
Linear equations word problems: graphs Get 3 of 4 questions to level up!
Graphing linear relationships word problems Get 3 of 4 questions to level up!

Intro to slope-intercept form

Intro to slope-intercept form (Opens a modal)
Slope and y-intercept from equation (Opens a modal)
Worked examples: slope-intercept intro (Opens a modal)
Linear equation word problems (Opens a modal)
Slope-intercept intro Get 3 of 4 questions to level up!
Linear equations word problems Get 3 of 4 questions to level up!

Graphing slope-intercept equations

Graph from slope-intercept equation (Opens a modal)
Graphing slope-intercept form (Opens a modal)
Graphing lines from slope-intercept form review (Opens a modal)
Graph from slope-intercept form Get 3 of 4 questions to level up!

Point slope form

Intro to point-slope form (Opens a modal)
Point-slope & slope-intercept equations (Opens a modal)
Point-slope form review (Opens a modal)
Point-slope form Get 3 of 4 questions to level up!

Standard form

Intro to linear equation standard form (Opens a modal)
Graphing a linear equation: 5x+2y=20 (Opens a modal)
Clarifying standard form rules (Opens a modal)
Converting from slope-intercept to standard form (Opens a modal)
Standard form review (Opens a modal)
Graph from linear standard form Get 3 of 4 questions to level up!
Convert linear equations to standard form Get 3 of 4 questions to level up!

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Important Questions Class 9 Maths Chapter 3

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Important Questions Class 9 Mathematics Chapter 3 – Coordinate Geometry

In Class 9 Mathematics, students will learn how to locate the points in a cartesian system or an XY plane throughout the chapter on coordinate geometry. This concept is useful for locating an object in a specific location. Locating points on a map or globe is its main application. In this chapter, you will also learn about terms related to the coordinate plane, as well as terms related to the Cartesian plane.

Extramarks is the preferred online learning destination for lakhs of students. We provide comprehensive NCERT-oriented study solutions, including chapter-wise notes, CBSE revision notes, questions and answers, etc. Students can prepare for all of the concepts included in the CBSE syllabus in a more effective and efficient manner by using our question bank of Important Questions for Class 9 Mathematics Chapter 3.Students are provided with a thorough explanation and key formulas to help them quickly review all topics. By practising questions from our question set of Mathematics Class 9 Chapter 3 Important Questions, students can improve their test preparation.

Our question and answer solution of Important Questions Class 9 Mathematics Chapter 3 will aid in your preparation for the upcoming board exams as well as assist you in getting excellent scores on the exams. We have focused on preparing you for the Class 9 exam using the CBSE curriculum. Your mathematical knowledge will be enhanced by regularly practising questions from our question bank of Important Questions for Class 9 Mathematics Chapter 3, which will also help you grasp the topic better.

In addition to our Class 9 Mathematics Chapter 3 Important Questions, Extramarks has a plethora of other study resources. Students can explore a variety of study materials from Class 1 to Class 12 to expedite their learning process and enhance their academic achievement.

Important Questions Class 9 Mathematics Chapter 3 – With Solutions

We advise students to solve questions from our question bank of Important Questions for Class 9 Mathematics Chapter 3 to gain a deeper understanding of the topics covered in Coordinate Geometry.

Our experienced mathematics faculty members have prepared step-by-step solutions after intensive study. By registering on the Extramarks website, students can access our question bank of Important Questions for Class 9 Mathematics Chapter 3 along with all solutions. The solutions should be practised by students regularly in order to gain maximum benefit from them.

Given below is a list of questionnaires and their answers from our question set of Important Questions for Class 9 Mathematics, Chapter 3.

Question 1: Point (–3, 5) lies in the

third quadrant
second quadrant
first quadrant
fourth quadrant

Solution 1: (B) Second Quadrant

Explanation:

(-3,5) is in the form of (-x,y).

In the given point (-3, 5), the abscissa is negative, and the ordinate is positive. So, it lies in the second quadrant.

Question 2: Signs of abscissa and ordinate of any given point in the second quadrant are respectively

Solution 2: (C) –, +

The signs of the abscissa and ordinate of a given point in the second quadrant are negative and positive respectively.

Question 3: Point (0, –7) lies

on the x-axis
in the fourth quadrant
on the y-axis
in the second quadrant

Solution 3: (C) on the y-axis

Explanation: Since the abscissa of the Point is 0, Point (0, –7) lies on the y-axis.

Question 4: Point (– 10, 0) will lie

in the negative direction of the x-axis
in the negative direction of the y-axis
in the third quadrant

Solution 4: (A) on the negative direction of the x-axis

Explanation: Point (– 10, 0) predominantly lies in the negative direction of the x-axis.

Question 5: Abscissa of all the given points on the x-axis is

Solution 5: (D) any number

Explanation: The abscissa of the points on the x-axis can be any number.

Question 6: Ordinate of all the given points on the x-axis is

Solution 6: (A) 0

Explanation: The ordinate of all the given points on the x-axis is 0.

Question 7: The Point at which the two coordinate axes converge is called the

Solution 7:

Explanation: The points where the two coordinate axes exactly meet are called the origin.

Question 8: A point both of whose coordinates are negative will be lying in

IV quadrant
III quadrant
II quadrant

Solution 8: (C) III quadrant

Explanation: A point whose both coordinates are negative will lie in the III quadrant.

Question 9: Points such as (1, – 1), (2, – 2), (4, – 5), (– 3, – 4)

will lie in IV quadrant
wil lie in III quadrant
will lie in II quadrant
will not lie in the same quadrant

Solution 9: (D) will not lie in the same quadrant

Points like (1, – 1), (2, – 2), (4, – 5) lie in the IV quadrant and (– 3, – 4) lie in III quadrants.

Question 10: If the y coordinate of a point taken as zero, then this Point always lies

in I quadrant
in II quadrant

Solution 10:

Explanation: We know that if the y-coordinate of a point is zero (ordinate), then this Point always lies on

Question 11: The given points (–5, 2) and (2, – 5) will lie in the

same quadrant
IV and II quadrants, respectively
II and IV quadrants, respectively
II and III quadrants, respectively

Solution 11: (C) on x-axis

(-5,2) is in the form (-x,y), so it lies in the II quadrant.

(2,-5) is in the form (x,-y), so it lies in the IV quadrant.

Question 12: If the perpendicular distance of the given point P from the x-axis is 5 units and the foot of the perpendicular lies in the negative direction of the x-axis, then the point P has

y – coordinate = – 5 only
y – coordinate = 5 only
x – coordinate = – 5
y – coordinate = 5 or –5

Solution 12: (D) y – coordinate = 5 or –5

Perpendicular distance from the x-axis = 5= Ordinate

The negative direction of the x-axis doesn’t decide the sign of the ordinate.

Question 13:

The points when the abscissa and ordinate have different signs will lie in

(a) I and II quadrants (b) I and III quadrants

Solution 13:(d)

Explanation: The points will be of the form (-x, y) or (x, – y)if the abscissa and ordinate have different signs and these points will lie in II and IV quadrants.

Question 14:

The Point whose ordinate is 4 and lies on K-axis is

(a)(1,4) (b) (0,4) (c) (4,0) (d) (4,2)

Solution 14: (b)

Explanation: Given the ordinate of any point is 4, and the Point lies on Y-axis, thus its abscissa is zero. Hence, the estimated Point is (0, 4).

Question 15:

Which of the following points P(0, 3), Q(l, 0), R(0, – 1), S(-5, 0) and T(1, 2) does not lie on the X-axis?

(a) Q, S and T (b)Q and S only (c)P, R and T (d)P and R only

Solution 15: (c)

Explanation: We are aware that a point will lie on the X-axis if it has the coordinates (x, 0), which means that its y-coordinate is zero. Points P (0, 3), R (0, -1), and T (1, 2) in this case does not lie on the X-axis since their y-coordinates are not zero.

Question 16:

The Point lying on the Y-axis at a distance of 5 units and in the negative direction of Y-axis is

(a) (0,5) (b) (-5,0) (c) (0,-5) (d) (5,0)

Solution 16: (C)

Explanation: The fact that the Point is on the X-axis indicates that its ^-coordinate is zero. Additionally, its y-coordinate is negative because it is 5 units away from the X-axis in the opposite direction.

Thus, the required Point is (0, – 5).

Question 17:

The perpendicular distance of the point P(3, 4) from the Y-axis is

(a) 3 (b) 5 (c) 4 (d) 7

Solution 17: (a)

Explanation: We are aware that a point’s abscissa, or x-coordinate, is the angle of that Point with respect to the Y-axis. As a result, point P(3, 4)’s distance from the Y-axis is equal to 3.

Question 18: The distance of the given Point (-3, -2) from the x-axis is

(a) 2 units

(b) 3 units

(d) 13 units

Solution 18: (a) 2 units

The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis.

Question 19: The distance of the given Point (-6, -2) from the y-axis is

(a) 6 units

(b) 8 units

(d) 10 units

Solution 19: (a) 6 units

The magnitude or absolute value of the Point’s x coordinate is its distance from the y axis.

Question 20: The abscissa and ordinate of the given Point with Coordinates (8, 12) is

(a) abscissa 12, ordinate 8

(b) abscissa 8, ordinate 12

(d) none of these

Solution 20: (a) abscissa 12 and ordinate 8

The abscissa is the y coordinate of the Point and the ordinate is the x coordinate value.

Question 21: The coordinate of origin in

(b) (0, y)

(d) none of these.

Solution 21: (c) (0, 0)

Explanation: For the origin, both abscissa and ordinate are 0.

Question 22: The distance of the Point (2,3) from y- axis is

(A) 2 units

(B) 3 units

(D) 13 units

Solution 22: (A) 2 units

Explanation: The magnitude or absolute value of the Point’s y coordinate is its distance from the x-axis. The magnitude or absolute value of the Point’s x coordinate is what determines how far the Point is from the y-axis.

Question 23: The point (-2, -1) lies in

(A) 1st quadrant

(B) 2nd quadrant

(D) 4th quadrant

Solution 23: (C) 3rd quadrant

Explanation: Negative x and y values relate to the third quadrant.

Question 24: The Point (3,0) lies on

(A) +ve x-axis

(B) – ve x-axis

(D) –ve y-axis

Solution 24 : (A) +ve x axis

Explanation: Because the x-coordinate is positive and the y-coordinate is zero.

Question 25: The distance of the Point (3, 5) from the x-axis is

(a) 3 units

(b) 4 units

(d) 6 units

Solution 25: (c) 5 units

Question 26: The Point (0, -5) lies on

(a) +ve x-axis

(b) +ve y-axis

(d) –ve y-axis

Solution 26: (d) –ve y-axis

Explanation: When the y coordinate is negative and the x coordinate is zero.

Question 27: The point (-2, 5) lies in

(a) 1st quadrant

(b) 2nd quadrant

(d) 4th quadrant

Solution 27: (b) 2nd quadrant.

Explanation: The x-values are negative and the y-values are positive in the second quadrant.

Question 28: The distance of the Point (3, 0) from the x-axis is

(b) 0 units

Solution 28: (a) 3 units.

Question 29: The points (other than the origin) whose abscissa is equal to the ordinate lie in

a) Quadrant II only
b) Quadrant I and II
c) Quadrant I & III
d) Quadrant I only

Solution 29: (c) quadrant I & III.

Explanation: In I and III quadrants, the axes will have the same sign.

Question 30:The perpendicular distance of the given point P(4,3) from the y axis is

c) 7 Units

Solution 30: (a) 3 units

The Point x coordinate indicates how far it is from the Y- axis.

Question 31:The area of triangle OAB with points 0(0,0), A(4,0) & B(0,6) is

a) 24 sq. units
b) 12 sq. units
c) 8 sq. unit
d) 16 sq. units

Solution 31: (b) 12 sq. units.

Explanation: The triangle’s area is equal to the product of its base and height.

Question 32: Plot the points A (2, 5), B (–2, 2) and C (4, 2) on graph paper. Join AB, BC and AC . Calculate the area of ∆ ABC .

Solution 32:

Abscissa of D = Abscissa of A = 2

Ordinate of D = Ordinate of B = 2

BC = (2 + 4) units = 6 units

AD = (5 – 2) units = 3 units

Area of ΔABC= 1 2 ×Base×Height

= 1 2 ×BC×AD

= 1 2 ×6×3

Hence, area of ∆ ABC is 9 square units

Question 33: Predict whether the given statements are True / False? Give justification for your answer.

(i) Point (3, 0) lying in the first quadrant.

(ii) Points (1, –1) and (–1, 1) lying in the same quadrant.

(iii) The coordinates of a point whose ordinate is – ½ and abscissa is 1 are – ½ , 1.

(iv) A point lying on the y -axis at 2 units distance from the x -axis. Its coordinates are (2, 0).

(v) (–1, 7) is a point lying in the II quadrant.

Solution 33:

(i) The Point (3, 0) lies in the first quadrant.

The ordinate of the given Point (3, 0) is given zero.

Hence, the Point must lie on the x-axis

(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.

(1, -1) lies in IV quadrant

while (-1, 1) lies in II quadrant.

(iii) The coordinates of a point for which ordinate is – ½ and abscissa is 1 are – ½ , 1.

The coordinates of a point for which ordinate is – ½ and abscissa is 1 is (1, -1/2).

(iv) A point is lying on the y -axis at a distance of 2 units from the x -axis. Its coordinates are (2, 0).

A point is lying on the y -axis at a distance of 2 units from the x -axis. Thus its coordinates are (0, 2).

(–1, 7) is a point in the II quadrant.

Question 34:

In which quadrant or axis on the following points will lie?

(-3, 5), (2,0), (2, 2), (-3,-6),(4,-1),

Solution 34:

(i) For point (-3, 5), the x-coordinate is negative while y-coordinate is positive, so it is lying in II quadrant.

(ii) For point (4,-1), the x-coordinate is positive while the y-coordinate is negative, so it lies in the IV quadrant.

(iii) In Point (2,0), the x-coordinate is positive while the y-coordinate is zero, so it lies on the X-axis.

(iv) In Point (2,2), both x-coordinate and y-coordinate are positive, so it lies in the I quadrant.

(v) In Point (-3, – 6), x-coordinate and y-coordinate both are negative, so it lies in III quadrant.

Question 35: Write the coordinates of the points P, Q, R, S, T and O from the figure given below.

Solution 35:

The coordinates of points P, Q, R, S, T and O are as follows:

Q = (-3, 0)

R = (-2, -3)

T = (4, -2)

Question 36: Without plotting the points find the quadrant in which they will lie, if

(i) ordinate is 5 while abscissa is – 3

(ii) abscissa is – 5 while ordinate is – 3

(iii) abscissa is – 5 while ordinate is 3

(iv) ordinate is 5 while abscissa is 3

Solution 36:

(i) The Point is (-3,5).

Hence, the Point is lying in the II quadrant.

(ii) The Point is (-5,-3).

Hence, the Point is lying in the III quadrant.

(iii) The Point is (-5,3).

(iv) The Point is (3,5).

Hence, the Point is lying in the I quadrant.

Question 37:

Three vertices of any rectangle ABCD are A (3, 1), B (–3, 1) and C (–3, 3). Plot these points on the graph paper and find the coordinates of the fourth vertex D . Also, find the area of rectangle ABCD .

Solution 37:

Let A (3, 1), B (–3, 1) and C (–3, 3) be three vertices of a rectangle ABCD .

Let the y -axis cut the rectangle ABCD at the points P and Q respectively.

Abscissa of D = Abscissa of A = 3.

Ordinate of D = Ordinate of C = 3.

∴ coordinates of D are (3, 3).

AB = ( BP + PA ) = (3 + 3) units = 6 units.

BC = ( OQ – OP ) = (3 – 1) units = 2 units.

Ar(rectangle ABCD ) = ( AB × BC )

= (6 × 2) sq. units

= 12 sq. units

Hence, the area of rectangle ABCD is 12 square units.

Question 38:

Which of the following points is lying on the Y-axis?

A(l, 1), B(1, 0), C(0, 1), D(0, 0), E(0, -1), F(-1, 0), G(0, 5), H(-7, 0) and I(3 ,3).

Thinking Process

The Point lying on the Y-axis means the x-coordinate of the Point will be zero. Check this condition for each and every given Point and find out the correct Point.

Solution 38:

We know that a point will be lying on the Y-axis, if its x-coordinate is zero. Given, x-coordinate of the points C(0, 1), D(0, 0), E(0,-1) and G(0, 5) are zero. So, these points tend to lie on the Y-axis. Also, D(0, 0) is the Point of intersection for both the axes, so we can consider that it lies on the Y-axis as well as on the X-axis.

Question 39: In the figure given below, LM is a parallel line to the y-axis at 3 units distance.

(i) What will be the coordinates of points P, R and Q?

(ii) What is the difference between the abscissas of points L and M?

Solution 39:

(i) The given coordinates are:

(ii) Since, all the points lying on the line have the same abscissa = 3.

The difference in abscissas of L and M is 0.

Question 40:

Find the possible coordinates of the Point

(i) which lies both on X and Y-axes .

(ii) whose ordinate is – 4 and lies on the Y-axis.

(iii) whose abscissa is 5 and lies on the X-axis.

Solution 40:

(i) The Point which lies both on the X and Y-axes is the origin and the coordinates are (0, 0).

(ii) The Point having ordinate – 4 and lies on Y-axis, i.e., the x-coordinate is zero, is (0,-4).

(iii) The Point whose abscissa is 5 and lies on X-axis, and the y-coordinate is zero, is (5, 0).

Question 41: See the figure given below and complete the following statements:

(i) The abscissa and the ordinate of any point B are _ _ _ and _ _ _, respectively.

Hence, the coordinates of B are (_ _, _ _).

(ii) The x-coordinate and the y-coordinate of any point M are _ _ _ and _ _ _,

respectively. Hence, the coordinates of M are (_ _, _ _).

(iii) The x-coordinate and the y-coordinate of any point L are _ _ _ and _ _ _,

respectively. Hence, the coordinates of L are (_ _, _ _).

(iv) The x-coordinate and the y-coordinate of any point S are _ _ _ and _ _ _,

respectively. Hence, the coordinates of S are (_ _, _ _).

Solution 41: (i) Since the distance of point B from the y – axis is 4 units, the x – coordinate or abscissa of point B is 4. The distance of point B from the x-axis is 3 units; therefore, the y – coordinate, i.e., the ordinate of point B is 3.

Thus, the coordinates of point B are (4, 3).

As in (i) above :

(ii) The x – coordinate and the y – coordinate of Point M are –3 and 4, respectively.

Hence, the coordinates of point M are (–3, 4).

(iii) The x – coordinate and the y – coordinate of point L are –5 and – 4, respectively.

Thus, the coordinates of any point L are (–5, – 4).

(iv) The x – coordinate and the y- coordinate of point S are 3 and – 4, respectively.

Thus, the coordinates of point S are (3, – 4).

Question 42: How will you describe the table lamp position on your study table to another person?

Solution 42:

We use two lines, a perpendicular and a horizontal line, to describe the location of the table lamp on the study table. Using the horizontal and perpendicular lines as the X and Y axes of the table, respectively, and the perpendicular line as the Y axis. Consider the intersection of the X and Y axes in one of the table’s corners as the origin. The table’s length is now its Y axis, and its width is its X axis. Create a point by connecting the line from the origin to the table light. It is necessary to compute the Point’s separation from the X and Y axes before expressing the results in terms of coordinates.

The table lamp will be in the coordinates (x, y) because the Point is separated from the X- and Y-axis by x and y, respectively.

Here, (x, y) = (15, 25)

Question 43: Write the answer for the following questions:

(i) What is the name of the lines that are drawn horizontally and vertically to represent the positions of all points in the Cartesian plane?

(ii) What are the names of the various components of the plane that these two lines form?

(iii) Indicate the name of the intersection location of these two lines.

Solution 43:

(i) The x-axis and y-axis are the names of the horizontal and vertical lines drawn to calculate the position of any point in the Cartesian plane.

(ii) The quadrants are the names of each section of the plane created by the x-axis and y-axis.

(iii)The origin is the location where these two lines intersect.

Question 44: Without plotting any of the points, indicate the quadrant in which they will lie, if

(i) the ordinate is 5 while abscissa is – 3

(ii) the abscissa is – 5 while the ordinate is – 3

(iii) the abscissa is – 5 while ordinate is 3

(iv) the ordinate is 5 while abscissa is 3

Solution 44:

Therefore, the Point lies in the II quadrant.

Therefore, the Point lies in the III quadrant.

Therefore, the Point lies in the I quadrant.

Question 45: Write the coordinates of any points marked on the axes in the figure given below.

Solution 45: Part 1

You can see that :

(i) The Point A is at + 4 units distance from the y – axis and at zero distance from the x-axis. Thus, the x – coordinate of A is 4, and the y – coordinate will be 0. Hence, the coordinates of Point A are (4, 0).

(ii) The coordinates of point B are (0, 3).

(iii) The coordinates of point C are (– 5, 0).

(iv) The coordinates of point D are (0, – 4).

(v) The coordinates of E are ( 2 3 ,0).

The y coordinate of any point situated on the x-axis is always zero because every Point on the x-axis is at zero distance from the x-axis. Any point on the x-axis, therefore, has coordinates of the form (x, 0), where x represents the distance of the Point from the y-axis. Similar to the x-axis, any point’s coordinates on the y-axis are of the form (0, y), where y is the Point’s distance from the x-axis.

Part 2: What are the coordinates of the origin O?

Its abscissa and ordinate are both zero since it is at zero distance from both axes. Consequently, the origin’s coordinates are (0, 0).

It is possible that you have noticed the correlation between a point’s coordinate sign and the quadrant in which it is located.

(i) Since the first quadrant is bounded by the positive x-axis and the positive y-axis, a point in the first quadrant will have the form ( +, +).

(ii) Because the second quadrant is bounded by the negative x-axis and the positive y-axis, a point in the second quadrant will have the form (-, +).

(iii)Because the third quadrant is bounded by the negative x-axis and the negative y-axis, a point in the third quadrant will have the form (-, -).

(iv) Given that the fourth quadrant is bounded by the positive x-axis and the negative y-axis, a point in the fourth quadrant will have the form (+, -).

Question 45: Write the answer to the following questions:

(i) What are the names of the lines that are drawn horizontally and vertically to represent the positions of every Point in the Cartesian plane?

Solution 45:

(i) The x-axis and y-axis are the names of the horizontal and vertical lines drawn to calculate the position of any point in the Cartesian plane.

(ii) Each section of the plane created by the x- axis and y-axis is referred to as a quadrant.

(iii) The Point where these two lines converge is called the origin.

Question 46: On which axis will the given points lie?

iii. (0, 6)

Solution 46:

(7,0) lies on X-axis since the y component is zero
(0, -3) lies on Y-axis since the x component is zero

iii. (0,6) lies on Y-axis since the x component is zero

(-5,0) lies on X-axis since the y component is zero

Question 47: In which quadrants will the given points lie?

iii. (-1, -2)

Solution 47:

The x component is positive, and the y component is negative. Hence the IV quadrant is (4,-2)
Due to the negative x component and the positive y component, the second quadrant is (-3,7).

iii. Due to the negative x and y components, the third quadrant is located at (-1,-2).

Since both the x and y components are positive, the Point (3, 6) lies in quadrant I.

Question 48: Does P (3, 2) represent the same Point as Q(2, 3), or not?

Solution 48: The points P(3,2) and Q(2,3) are not the same, hence the answer is no. Unlike Q, which has an x component of 2 and a y component of 3, the first one has an x component of 3 and a y component of 2.

Question 49: Locate the given points (5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and

(6, 1) in the Cartesian plane.

Solution 49 : We take 1cm = 1 unit; we now draw the x-axis and the y – axis. The positions of

the given points are shown by dots in figure below

You can see that the positions of (0, 5) and (5, 0) are not identical. The placements of (2, 5) and (5, 2) are also different. Additionally, the positions of (-3, 5) and (-5, -3) are different. You can demonstrate this by using multiple instances to show that if x y, then the positions of (x, y) in the Cartesian plane are not the same (y, x). The position of (y, x) will be different from the position of (y, x) if the coordinates x and y are switched (x, y). This implies that it’s crucial to consider x and y’s order when (x, y).

Therefore, (x, y) is called an ordered pair. The ordered pair (x, y) ≠ ordered pair (y, x) if x ≠ y. Also (x, y) = (y, x), if x = y.

Question 52: Find the coordinates of Point equidistant from the given two points P(3,0) and Q(-3,0). How many points possibly satisfy this condition?

Solution 52: All the points on the Y-axis satisfy this condition.

Question 53: Plot the following given ordered pairs (x, y) of numbers as points in the Cartesian plane. Using the scale 1cm = 1 unit on the axes.

Solution 53 : The pairs of numbers represented in the table can be indicated by the points

(– 3, 7), (0, –3.5), (– 1, – 3), (4, 4) and (2, – 3). The locations of the given points are shown

by dots in the figure given below.

Question 54: Name each part of the given plane formed by the Vertical and horizontal lines.

Solution 54: The vertical line is called the y-axis and the horizontal line is called the x-axis. And these form four quadrants.

Question 55: Write the mirror image of the given Point (2, 3) and (-4, -6) with respect to the x-axis.

Solution 55: The mirror image of the given Point (2, 3) is (2, -3) with respect to the x-axis.

The mirror image of the Point (-4, -6) is (-4,6) with respect to the x-axis.

Question 56: Write the abscissa and ordinate of a point (-3, -4)

Solution 56: The Abscissa will be -3 and ordinate will be -4

Question 57: State the quadrant in which each of the following points will lie:

(ii) (-7,11)

(iii) (-6, -4)

(iv) (-5, -5)

Solution 57: (2, 1) lie in the I quadrant

(-7, 11) lie in the II Quadrant

(-6, -4) lie in the III Quadrant

(-5, -5) lie in the III Quadrant

Question 58: What is the name of the horizontal and vertical lines which are drawn to determine the position of any given point in the Cartesian plane?

Solution 58: The horizontal line is called the x-axis while the vertical line is called the y – axis

Question 59: List the points on the plane that do not fall into any of the four quadrants.

Solution 59: The points in a plane that do not belong to any one of the quadrants is origin and are denoted by point O (0,0).

Question 60: Which of the given points belong to the x-axis?

(a) (2, 0) (b) (3, 3) (c) (0, 1) (d) (-2, 0)

Solution 60: (2, 0) and (-2, 0) belong to the x- axis.

For the Point to belong to the y-axis, the y-component must be zero.

Question 61: Which of the given points belongs to the 1st quadrant

(a) (3, 0) (b) (1, 2) (c) (-3, 4) (d) (3, 4)

Solution 61: (1, 2) and (3, 4) belong to the 1st quadrant.

Question 62: Which of the given points belongs to 3rd quadrant

(a) (1, 3) (b) (-1, -3) (c) (0, 4) (d) (-4, -2)

Solution 62: (-1, -3) and (-4, -2) belong to the 3rd quadrant.

Question 63: Answer each of the following questions:

(i) In order to locate any point in the Cartesian plane, what is the name of the horizontal and vertical lines that are drawn?

Solution (i) : The x-axis and the y-axis are the lines that are drawn to determine the positions of any points in the Cartesian plane, respectively.

(ii) What are the names of the various components of the plane that these two lines form?

Solution (ii) : The term “quadrant” refers to each section of the plane that is created by the x- and y-axes.

(iii) Indicate the name of the intersection location of these two lines.

Solution (iii): The origin, symbolised by O, is the location where the x- and y-axes connect (0,0).

Question 64: Find the ordered pairs of the linear equation

and plot them as ‘how many such ordered pairs can be present and plotted?

Solution 64: The given equation is

The equation will hold if

thus, (0, 4),

thus, (1, 2),

thus,(2, 0) ,

i.e. (3, -2)…

Likewise, (4,-4), (5,-6), (-1,6), (-2,8) etc. also. These are a few ordered pairs which are

valid solutions. And such ordered pairs are infinite.

Question 65: What is coordinate geometry?

Solution 65: In order to present geometric forms in a two-dimensional plane and learn about their properties, coordinate geometry is a crucial area of mathematics. In order to get a basic concept of coordinate geometry, we’ll try to learn about the coordinate plane and a point’s coordinates here.

Question 66: What is a Coordinate plane?

Solution 66: In order to make it simple to locate the points, a cartesian plane divides the plane space into two dimensions. The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axis of the coordinate plane. The origin is the place where these coordinate axis connect, and they divide the plane into four quadrants (0, 0). Additionally, any point in the coordinate plane is denoted by the coordinates (x, y), where x represents the Point’s position in relation to the x-axis and y represents its position in relation to the y-axis.

Question 67: What are the properties of a point?

Solution 67: The properties of the Point in the coordinate plane’s four quadrants are as follows:

The origin O is the location where the x- and y-axes intersect, and its coordinates are (0, 0).
The positive x-axis is to the right of the origin O, while the negative x-axis is to the left of the origin O. Additionally, the positive and negative y-axis are located above and below the origin O, respectively.
The first quadrant’s Point (x, y) is plotted with reference to the positive x-axis and the positive y-axis because it has both positive values.
With reference to the negative x-axis and positive y-axis, the point (-x, y) in the second quadrant is drawn.
Plotting is done with reference to the negative x-axis and negative y-axis for the Point depicted in the third quadrant (-x, -y).
The positive x-axis and the negative y-axis are used to plot the Point (x, -y) that is located in the fourth quadrant.

Question 68: Explain the coordinates of a point.

Solution 68:

Image source: Internet

An address that aids in locating a spot in space is a coordinate. The coordinates of a point in a two-dimensional space are (x, y). Let’s note these two crucial terms right now.

Abscissa: The distance from the origin along the x-axis is represented by the x value at the Point (x, y).
Ordinate: It is the y value at the coordinates (x, y) and the angle at which the Point lies in relation to the x-axis, which runs parallel to the y-axis.

A point’s coordinates can be used for a variety of tasks, including calculating distance, midpoint, a line’s slope, and its equation.

Question 69: Write the distance formula in coordinate geometry.

Solution 69: The square root of the sum of squares of the difference between the x coordinate and the y coordinate of the two supplied points is equal to the distance between two points (x1, y1) and (x2, y2) in this example. The following is a formula for calculating the separation between two points.

D = (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2

Benefits of Solving Important Questions Class 9 Mathematics Chapter 3

The benefits of answering questions from our Chapter 3 Class 9 Mathematics important questions are listed below.

Our Important Questions Class 9 Mathematics Chapter 3 question bank follows the NCERT exam style and is based on the recent CBSE syllabus. It thus includes questions with a variety of formats, such as multiple-choice questions (MCQs), fill-in-the-blank questions, and long and short responses in order to expose students to actual board exam paper patterns. This encourages pupils to perform better on exam day and earn higher grades.
Mathematics subject experts with years of experience have prepared the answers. Additionally, experts work continuously to review and improve the responses. As a result, students may confidently rely on our solutions as they adhere to recent CBSE syllabus and exam guidelines.
Students can completely review the ideas presented in the chapter by practising the various high-level questions included in the Important Questions Class 9 Mathematics Chapter 3. This will enable them to review the material once more and provide an opportunity for them to identify and correct any weaknesses before their final exams. Maintain a strict study routine as well if you want to pass with flying colours.
While practising these questions students will get used to the questions with varying levels of difficulty and some of them are tweaked to test the understanding level of the students, questions are also repeated to strengthen their understanding and even provide enough practice to improve their speed along with analytical skills.
Scoring a high percentage is not difficult. You just require the right strategies and correct understanding of the concepts to ensure 100% result in Mathematics.

The answers given to all questions in our Class 9 Mathematics Chapter 3 Important Questions adequately cover all of the key points with explanations.

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Q.1 Plot the following points in a Cartesian plane:

(-2,4), (3,-1), (-1, 0), (1, 2) & (-3, -5)

Marks :4 Ans

Q.2 Which of the following points:

B(1, 0), C(0,1 ), E (-1, 0), F ( 0, -1), G (4, 0), H (0, -7)

(i) lie on x ?axis?

(ii) lie on y ? axis?

Marks :3 Ans

(i)The point whose ordinate is 0 lies on x axis.

Therefore, the point B (1,0), E (-1,0), G(4,0) lie on x axis.

(ii) The point whose abscissa is 0 lies on y axis.

Therefore, the points C (0,1), F (0,-1) , H (0,-7) lie on y-axis.

Q.3 See the figure, and write the following:

1) The coordinates of B.

2) The point identified by the point (-3, -5).

3) The abscissa of point D.

4) The ordinate of the point E.

5) The point identified by the coordinates (2, -4).

1) Coordinate of B(2, 2).

2) A(-3, -5)

3) Abscissa of point D is 5.

4) Ordinate of point E is -4.

5) E(2, -4)

Q.4 The coordinates of the vertices of the triangle ABC, as shown in the figure, are __________________.

(2, 2), (1,3) and (1, 0) / (2, 2), (1, 3) and (1, 0)
(2, 2), (1, 3) and (0, 1) / (2, 2), (1, 3) and (0, 1)
(2, 2), (1, 3) and (1, 0) / (2, 2), (1, 3) and (1, 0)
(2, 2), (?1, 3) and (0, 1) / (2, 2), (1, 3) and (0, 1)

Marks :1 Ans

(2, 2), (1, 3) and (1, 0)

Q.5 After walking 6 units in the direction parallel to the x-axis to the left of the origin, Jacob reaches point P. If he started from the point (1, 2), then the coordinates of point P are _____________.

( 5, 2) (5, 0)
(4, 2) (4, 2)

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Faqs (frequently asked questions), 1. which is the best mathematics guide for class 9 mathematics.

Students are advised to first study the syllabus from NCERT textbooks and then practise questions from NCERT exemplar books. Along with that students should register with Extramarks to get access to a comprehensive set of study materials including NCERT chapter-wise solutions, CBSE revision notes, questions and answers solutions, CBSE solved sample papers, etc. One of the most important study materials is our question bank of Important Questions Class 9 Chapter 3 Mathematics and other chapters that will give a consolidated set of questions from different sources. It’s a crucial study aid as it will help students to practise a lot of exam oriented questions and significantly improve their scores in final exams.

2. How much time should a Class 9 student spend practising Mathematics?

The time limit is not important for any of the subjects, especially Mathematics and Science. Mathematics is a core subject of many career streams and its application will be required in daily life. So it’s important for students to have a good hold on the subject.

We recommend students to devote regular study hours for Mathematics and revise the Class 9 Mathematics curriculum thoroughly.

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CBSE Class 9 Maths Case Study Questions PDF Download

Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams.

Case study questions play a pivotal role in enhancing students’ problem-solving skills. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

Table of Contents

CBSE Class 9th MATHS: Chapterwise Case Study Questions

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of Class 9 Maths

Case Study Questions for Chapter 1 Number System
Case Study Questions for Chapter 2 Polynomials
Case Study Questions for Chapter 3 Coordinate Geometry
Case Study Questions for Chapter 4 Linear Equations in Two Variables
Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
Case Study Questions for Chapter 6 Lines and Angles
Case Study Questions for Chapter 7 Triangles
Case Study Questions for Chapter 8 Quadrilaterals
Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
Case Study Questions for Chapter 10 Circles
Case Study Questions for Chapter 11 Constructions
Case Study Questions for Chapter 12 Heron’s Formula
Case Study Questions for Chapter 13 Surface Area and Volumes
Case Study Questions for Chapter 14 Statistics
Case Study Questions for Chapter 15 Probability

Checkout: Class 9 Science Case Study Questions

And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net

The above Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

3. Definition of nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type

(and their combinations) where x and y are natural number and a and b are integers.

5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26 Periods)

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

Read the case study thoroughly and understand the problem statement before attempting to solve it.
Identify the relevant data and extract the necessary information for your solution.
Break down complex problems into smaller, manageable parts to simplify the solution process.
Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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RS Aggarwal Solutions Class 9 Chapter 5 Coordinate Geometry

RS Aggarwal Solutions for Class 9 Maths Book Chapter 5 Coordinate Geometry are available here. Study path has prepared solutions of all the exercises of the chapter by our expert math teachers to help you to get good marks in exams. This lesson has a ton of questions that are very important from the examination point of view.

We at Study Path solved each questions step by step with detailed explanations. Students must practice from practice these problems to score high marks in Maths. Below we have listed the Class 9 RS Aggarwal Solutions Chapter 5 Coordinate Geometry Exercise 5 and Multiple Choice Questions (MCQs).

Class 9 RS Aggarwal Solutions Chapter 5 Coordinate Geometry

Class 9 rs aggarwal solutions chapter 5 exercise 5.

RS Aggarwal Solutions Class 9 Chapter 5 Coordinate Geometry Exercise 5 00001

Class 9 RS Aggarwal Solutions Chapter 5 MCQs

RS Aggarwal Solutions Class 9 Chapter 5 Coordinate Geometry Multiple Choice Questions MCQs 00001

Class 9 Maths Chapter 3 Coordinate Geometry MCQs

Class 9 Maths Chapter 3 Coordinate Geometry MCQs are available here online. The objective questions are provided with their respective answers and detailed explanations. The Coordinate Geometry MCQs are prepared for Class 9 students as per the latest exam pattern. Students can practise these questions and score good marks in the final exam. These selective questions are given here, as per the CBSE syllabus (2022-2023) and NCERT guidelines. Also, check Important Questions for Class 9 Maths .

Download the below PDF to get more MCQs on Class 9 Maths Chapter 3 Coordinate Geometry.

Class 9 Maths Chapter 3 Coordinate Geometry MCQs – Download PDF

MCQs on Class 9 Maths Chapter 3 Coordinate Geometry

Students can solve the multiple-choice problems given below to increase their problem-solving skills. Each question has 4 multiple options. Students need to choose the right answer.

1) The name of the horizontal line in the cartesian plane which determines the position of a point is called:

d. Quadrants

2) The name of the vertical line in the cartesian plane which determines the position of a point is called:

3) The section formed by horizontal and vertical lines determining the position of the point in a cartesian plane is called:

4) The point of intersection of horizontal and vertical lines determining the position of a point in a cartesian plane is called:

5) If the coordinates of a point are (0, -4), then it lies in:

c. At origin

d. Between x-axis and y-axis

Explanation: Since, x=0 and y=-4. Hence, the point will lie in the negative y-axis 4 units far from the origin.

6) If the coordinates of a point are (3, 0), then it lies in:

Explanation: Since, x = 3 and y = 0, therefore, the point will lie at the positive x-axis 3 units far from the origin.

7) If the coordinates of a point are (-3, 4), then it lies in:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Explanation: Since x = -3 and y = 4, then if we plot the point in a plane, it lies in the second quadrant.

8) If the coordinates of a point are (-3, -4), then it lies in:

Explanation: Since, x = -3 and y = -4, then if we plot the point in a plane, it lies in the third quadrant.

9) Points (1, 2), (-2, -3), (2, -3);

b. Do not lie in the same quadrant

10) If x coordinate of a point is zero, then the point lies on:

11) Signs of the abscissa and ordinate of a point in the second quadrant are respectively

b. +, –

d. -, –

Explanation: The signs of abscissa (x-value) and ordinate(y-value) in the second quadrant are – and + respectively.

12) The point (-10, 0) lies in

a. Third quadrant

b. Fourth quadrant

c. On the negative direction of the x-axis

d. On the negative direction of the y-axis

Explanation: The point (-10, 0) lies in the negative direction of the x-axis.

13) A quadrant in which both x and y values are negative is

Explanation: In the third quadrant, both the abscissa and ordinate values are negative. Example (-2, -2), which lies in the third quadrant.

14) Abscissa of all the points on the x-axis is

d. Any number

Explanation: Abscissa of all the points on the x-axis can be any number. The coordinates of any point on the x-axis is (x, 0), where x can take any value.

15) Ordinate of all points on the x-axis is

Explanation: The ordinate of all points on the x-axis is 0. We know that the coordinates of any point on the x-axis is (x, 0). Here, the abscissa can take any value and the ordinate is zero.

16) Abscissa of a point is positive in

a. I quadrant

b. I and II quadrants

c. II quadrant only

d. I and IV quadrants

Explanation: In a coordinate plane, x can take positive values in the first and fourth quadrants. For example, (2, 2) and (2, -4) lie on the first and fourth quadrants, respectively.

17) Points (1, -1), (2, -2), (4, -5), (-3, -4)

a. lie in II quadrant

b. lie in III quadrant

c. lie in IV quadrant

d. Does not lie in the same quadrant

Explanation: The point (1, -1), (2, -2) and (4, -5) lies in the fourth quadrant, where (-3, -4) lies in the third quadrant.

18) Abscissa of all the points on the y-axis is

Explanation: The abscissa of all the points on the y-axis is 0. We know that the coordinates of any point on the y-axis is (0, y). Here, the ordinate can take any value and the abscissa is zero.

19) Ordinate of all the points on the y-axis is

Explanation: The ordinate of all the points on the y-axis can be any number. The coordinates of any point on the y-axis is (0, y). Here, abscissa can take only the value of 0 and the ordinate can take any value.

20) The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is

Explanation: The coordinates of any point on the y-axis is (0, y).

Hence, abscissa should be 0.

Given that, the point lies in the negative direction of the y-axis. Hence, the value of y should be negative.

Therefore, the point which lies on the y-axis at a distance of 5 units in the negative direction is (0, -5).

Class 9 Related Articles on Coordinate Geometry

Coordinate Geometry Class 9 Notes – Chapter 3
Coordinate Geometry Formulas
Important Questions Class 9 Maths Chapter 3-Coordinate Geometry
Two Dimensional Coordinate Geometry

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Coordinate Geometry Class 9 Extra Questions Short Answer Type 2. Question 1. Without plotting the points indicate the quadrant in which they lie, if : (i) ordinate is 5 and abscissa is - 3. (ii) abscissa is -5 and ordinate is - 3. (iii) abscissa is - 5 and ordinate is 3. (iv) ordinate is 5 and abscissa is 3.
Coordinate Geometry
Math; Class 9 (OD) Unit 5: Coordinate Geometry. 2,200 possible mastery points. Mastered. Proficient. Familiar. Attempted. Not started. Quiz. Unit test. ... Quadrants on the coordinate plane Get 5 of 7 questions to level up! Slope of a line. Learn. Intro to slope (Opens a modal) Positive & negative slope (Opens a modal) Worked example: slope ...
Important Questions Class 9 Maths Chapter 3
Important Questions Class 9 Mathematics Chapter 3 - Coordinate Geometry. In Class 9 Mathematics, students will learn how to locate the points in a cartesian system or an XY plane throughout the chapter on coordinate geometry. This concept is useful for locating an object in a specific location.
CBSE Class 9 Maths Case Study Questions PDF Download
Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams. Case study questions play a pivotal role in enhancing students' problem-solving skills.
Coordinate Geometry Class 9 Notes with Solved Examples
CBSE Class 9 Maths Coordinate Geometry Notes:-Download PDF Here Coordinate geometry is significant because it provides a link between geometry and algebra through line graphs and curves. Coordinate geometry is useful in mathematics because it allows us to locate points on any plane.
NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry
Here you will get complete NCERT Solutions for Class 9 Maths Chapter 3 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.
Class 9 : Coordinate Geometry- Case Study Questions
Use Code PN10 to unlock the class. In this session, Prashant Sir will discuss on important concepts and will take practice through Polls on Coordinate Geometry. This session will be helpful for aspirants preparing for CBSE class 9th exam. This session will be conducted in Hinglish and notes will provided in English.
RS Aggarwal Solutions Class 9 Chapter 5 Coordinate Geometry
RS Aggarwal Solutions for Class 9 Maths Book Chapter 5 Coordinate Geometry are available here. Study path has prepared solutions of all the exercises of the chapter by our expert math teachers to help you to get good marks in exams. This lesson has a ton of questions that are very important from the examination point of view.
Class 9 Maths Chapter 3 Coordinate Geometry MCQs
Chapter 3. Students can solve the multiple-choice problems given below to increase their problem-solving skills. Each question has 4 multiple options. Students need to choose the right answer. 1) The name of the horizontal line in the cartesian plane which determines the position of a point is called: a. Origin.

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Important Questions for Class 9 Maths Coordinate Geometry

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