CBSE Class 9 Maths Important Questions - Chapter 3 Coordinate Geometry

Section - A

1 On which axes do the given points lie?

i. (7, 0)

ii. (0, -3)

iii. (0, 6)

iv. (-5, 0)

Ans:

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?

i. (4, -2)

ii. (-3, 7)

iii. (-1, -2)

iv. (3, 6) 

Ans:

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

a) 3 Units

b) 4 Units

c) 5 Units

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?

Ans:

P (1,1)

Q (-3,0)

R (-2,-3)

S (2,1)

T (4,-2)

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

i. A (5,3)

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.

i. A(2,3)

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

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.

Ans:

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

(b) origin

(c) null 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

(c) 5 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

(c) 2 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

(c) abscissa 0 and ordinate 20

(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

(a) (X, 0)

(b) (0, y) 

(c) (0, 0)

(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

(C) 5 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

(C) 3rd quadrant

(D) 4th quadrant

Ans: (C) 3rd quadrant

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

8. The point (3,0) lies on

(A) +ve x axis

(B) – ve x axis

(C) + ve y 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

(c) 5 units

(d) 6 units  

Ans: (c) 5 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.

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

(a) +ve x- axis

(b) +ve y- axis

(c) –ve x- 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

(c) 3rd 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

(a) 3 units

(b) 0 units

(c) 9 units

(d) none of these

Ans: (a) 3 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.

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: 

(i) (2, 1)

(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

(i) (2,3)

(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?

Ans: 

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.

Ans: 

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

Ans:

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. 

Ans: 

(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.

Ans: 

(-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.

Ans:

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.

Ans:

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

(a) (3, 4)

(b) (-3, -4)

(c) (0, -5)

(d) (2, -5)

(e) (2, 0) 

Ans: 

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?

Ans: 

Yes a straight line is obtained by joining these points.

Important Questions for Class 9 Maths Chapter 3 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.

Plotting a Point 

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

Solution

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.

Important Formula Covered in Class 9 Maths Chapter 3 - Coordinate Geometry

List of Important Questions for Class 9 Maths Chapter 3 Cordinate Geometry

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)