NCERT Exemplar Class 9 Maths Solutions Chapter 3 Coordinate Geometry

There is a saying in Mathematics that the area where algebra and geometry intersect is called coordinate geometry. In coordinate geometry, every point has a story, and the graph will show the visual representation. In Chapter 3 of the NCERT exemplar class 9 maths solutions, students will learn about coordinate geometry and its real-life applications. Furthermore, they will learn about the Cartesian system, the origin, quadrants, and plotting points on graph paper using given coordinates. After finishing the NCERT textbook exercises, when students need an extra resource for practice, these class 9 NCERT exemplars become handy.

The NCERT exemplar maths solutions for class 9 of coordinate geometry will build a strong base of this chapter early so that students have no problem dealing with this chapter in higher classes. Careers360 teachers have prepared these solutions, explaining each step alongside the relevant formulas so that the learning process becomes easier. Students can also check the NCERT solutions for class 9 for more information.

Exercise: 3.1 Total Questions: 24 Page Numbers: 25-27

Question:1

Point (–3, 5) lies in the

(A) first quadrant
(B) second quadrant
(C) third quadrant
(D) fourth quadrant

Answer: [B]
Solution:

We know that in
First quadrant : (+, +)
Second quadrant : (–, +)
Third quadrant : (–, –)
Fourth quadrant : (+, –)
Thus, the value of x is –3 and y is 5
So, that point (–3, 5) lies in the second quadrant.
Therefore, option (B) is correct.

Question:2

Signs of the abscissa and ordinate of a point in the second quadrant are respectively
(A) +, +
(B) –, –
(C) –, +
(D) +, –

Answer: [C] –, +
Solution:

We know that the x-coordinate is called the abscissa, and the y-coordinate is also called the ordinate.
Thus, in the second quadrant abscissa is negative, and the ordinate is positive.
So that, the in the second quadrant, signs of the abscissa and ordinate is ( –, +)
Therefore, option (C) is correct.

Question:7

The point at which the two coordinate axes meet is called the
(A) abscissa
(B) ordinate
(C) origin
(D) quadrant

Answer: [C] origin
Solution.


We know that the coordinate axis x and y divide the plane into four parts called quadrants and the point of intersection of the axis is called the origin.
Coordinate of the origin are (0, 0).
Abscissa is the x-axis (horizontal) coordinate
Ordinate is the y-axis (vertical) coordinate
Therefore, option (C) is correct

Question:8

A point both of whose coordinates are negative will lie in
(A) I quadrant
(B) II quadrant
(C) III quadrant
(D) IV quadrant

Answer: (C) III quadrant
Solution.
We know that the coordinates of a point are of the form (+, +) in the first quadrant.
(-, +) in the second quadrant
(-,-) in the third quadrant and
(+, -) in the fourth quadrant.
Where + denotes a positive real number and - denotes a negative real number. So that we can say that two coordinates that are negative lie in the third quadrant.

Therefore, option (C) is correct.

Question:9

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) do not lie in the same quadrant

Answer:

Answer: [D] Do not lie in the same quadrant
Solution.

We know that coordinates of a point are of the form (+, +) in the first quadrant
(–, +) in the second quadrant
(–,–) in the third quadrant and
(+, –) in the fourth quadrant.
Where + denotes a positive real number and - denotes a negative real number.
So, points $(1,-1),(2,-2)$ and $(4,-5)$ all lie in the IV quadrant but $(-3,-4)$ lies in IIIrd quadrant.
So, we can say that the given points do not lie in the same quadrant.
Therefore, option (D) is correct

Question:10

If the y coordinate of a point is zero, then this point always lies
(A) In I quadrant
(B) In II quadrant
(C) on x - axis
(D) on y-axis

Answer: (C) on x - axis

We know that coordinate of x axis are (x, 0)
i.e., the y coordinate is zero on the x axis.
So, if the y-coordinate of a point is zero, then this point always lies on the x-axis.
Therefore, option (C) is correct

Question:11

The points $(-5,2)$ and $(2,-5)$ lie in the
(A) same quadrant
(B) II and III quadrants, respectively
(C) II and IV quadrants, respectively
(D) IV and II quadrants, respectively

Answer: (C) II and IV quadrants, respectively
We know that
A point in the first quadrant is (+, +)
A point in the second quadrant is (–, +)
A point in the third quadrant is (–, –)
A point in the fourth quadrant is (+, –)

Here $(-5,2)$ and $(2,-5)$ both are lie in the different quadrants.
Point $(-5,2)$ lies in the II quadrant and point $(2,-5)$is lies in the IV quadrant.

Question:12

If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of the x-axis, then the point P has

(A) x coordinate = -5
(B) y coordinate = 5 only
(C) y coordinate = -5only
(D) y coordinate = 5 or -5

Answer: (D) y coordinate = 5 or -5
Solution.
We know that the perpendicular distance of any point from the x-axis gives the y-coordinate of that point.
i.e., the x coordinate is always perpendicular to the y-axis.


(A) Here x-coordinate is -5. It lies on the negative direction of the x-axis, so it is incorrect
(B) Here y-coordinate is 5. It lies on the positive direction of the y-axis and is perpendicular to the x-axis, so it is incorrect
(C) Here y-coordinate is -5. It lies on the negative direction of the y-axis and is perpendicular to the x-axis.
So it is incorrect
(D) Here y-coordinate is 5 or -5, i.e., the perpendicular distance can be in the II quadrant or III quadrant. So that we can say the point P has y-coordinate 5 or -5
Therefore, option (D) is correct

Question:13

On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO, which of the following figures is obtained?
(A) Square
(B) Rectangle
(C)Trapezium
(D) Rhombus

Answer: (B) Rectangle
Solution.

(C)Rectangle: We know that in the rectangle, opposite sides are equal in measurement and are parallel to each other.
So here OA = BC = 3 units and OC = AB = 4 units
Hence, it is a rectangle.

Question:14

If $P(-1,1),Q(3,-4),R(1,-1),S(-2,-3)$ and $T(-4,4)$ are plotted on the graph paper, then the point(s) in the fourth quadrant are:
(A) P and T
(B) Q and R
(C) Only S
(D) P and R

Answer: (B) Q and R


(A) Here point $P(-1,1)$ and $T(-4,4)$ lie in II quadrant.
(B) Here point $Q(3,-4)$ and $R(1,-1)$ lie in IV quadrant.
(C) Here point $S(-2,-3)$ lies in III quadrant
(D) Here point $P(-1,1)$ and $R(1,-1)$ both lie in different quadrants
P lies in II quadrant and R lies in IV quadrant.
Therefore, option (B) is correct

Question:16

If P (5, 1), Q (8, 0), R (0, 4), S (0, 5) and O (0, 0) are plotted on the graph paper, then the point(s) on the x-axis are:
(A) P and R
(B) R and S
(C) Only Q
(D) Q and O

Answer: (D) Q and O
Plotting the given points, we have:


(A) Points P and R lie on a different axis. So it is incorrect.
(B) Points R and S lie on the y-axis because, on the y-axis, the x coordinate is always zero. So it is incorrect.
(C) Point Q (8, 0) lies on the x-axis because on the x-axis, the y coordinate is always zero. So it is incorrect.
(D) Points Q and O have a y-coordinate as 0, so they are plotted on the x-axis. So this is correct.
Therefore, option (D) is correct

Question:17

Abscissa of a point is positive in
(A) I and II quadrants
(B) I and IV quadrants
(C) I quadrant only
(D) II quadrant only

Answer: (B) I and IV quadrants
Solution.


The abscissa is the x-axis (horizontal) coordinate
(A) We know that abscissa is positive and negative in I quadrant and II quadrants respectively, so this option is incorrect.
(B) Abscissa of a point is positive in 1 quadrant and IV quadrants. Because in I quadrant we have (+, +) and in II quadrant we have (+, –).
So, the abscissa is positive in both quadrants.
Hence this option is correct.
(C) We know that in the I and IV quadrant, the abscissa is positive.
So this option is incorrect.
(D) In II quadrant, abscissa is negative.
So this option is incorrect.
Therefore, option (B) is correct.

Question:19

In Fig. 3.1, coordinates of P are

(A) $(-4,2)$
(B) $(-2,4)$
(C) $(4,-2)$
(D) $(2,-4)$

Answer: (B) (-2, 4)
Solution.

From the figure, we can see that:
Here x coordinate is -2, and the y coordinate is 4
So that coordinate of point P(-2, 4).
Therefore, option (B) is correct

Question:20

In Fig. 3.2, the point identified by the coordinates (–5, 3) is

(A) T
(B) R
(C) L
(D) S

Answer: (C) L(-5, 3)
Hint
Solution.


Coordinate of point $T(3,-5)$
Coordinate of point $R(-3,5)$
Coordinate of point $L(-5,3)$
Coordinate of point $S(-5,3)$
Therefore, option (C) is correct

Exercise: 3.2 Total Questions: 1 Page Numbers: 28

Question:1

Write whether the following statements are True or False. Justify your answer.
Point (3, 0) lies in the first quadrant.

Answer: False
Solution.
False, because point (3, 0) lies on the x-axis.

It does not lie in the first quadrant.
Points which lie in the first quadrant have both x and y coordinates as positive.
Examples: (1, 3) (2, 4) etc.
Therefore, the given statement is False.

Question:2

Write whether the following statements are True or False. Justify your answer.
Points (1, -1) and (-1. 1) lie in the same quadrant.

Answer: False
Solution.

False, point (1, -1) and (-1. 1) lie in the different quadrants.
Point (1, -1) lies in the IV quadrant and point (-1. 1) lies in the II quadrant.
Therefore, the given statement is False.

Question:5

Write whether the following statements are True or False. Justify your answer. (-1, 7) is a point in the II quadrant.

Answer: True
Solution.

We know that signs in II quadrant are (-, +), and here we have the point as (-1, 7)
i.e., the x-coordinate is negative and the y-coordinate is positive.
Therefore, the given statement is True.

Question:2

Plot the following points and write the name of the figure obtained by joining them in order: $P(-3,2),Q(-7,-3),R(6,-3),S(2,2)$

Answer:

Solution.
The given points
$P(-3,2),Q(-7,-3),R(6,-3),S(2,2)$
are plotted as follows:

From the figure we can see that PS is parallel to QR. Distance between them is fixed, i.e., 5 units.
Also, PQ and RS are non-parallel.
Hence, the obtained figure is a trapezium.

Question:4(i)

Plot the following points and check whether they are collinear or not : (1, 3), (– 1, – 1), (– 2, – 3)

Answer:

Plotting the given points:
(1, 3), (– 1, – 1), (– 2, – 3)

Hence, these points lie on a straight line.
These points are collinear

Question:4(ii)

Plot the following points and check whether they are collinear or not :
(1, 1), (2, – 3), (– 1, – 2)

Answer: Non-Collinear
The given points can be plotted as follows:
(1, 1), (2, – 3), (– 1, – 2)

The given points do not lie on the same straight line.
Hence, they are non-collinear

Question:4(iii)

Plot the following points and check whether they are collinear or not :
(0, 0), (2, 2), (5, 5)

Answer: Collinear
Plotting the given points:
(0, 0), (2, 2), (5, 5)

Hence, these points lie on a straight line.
These points are collinear.

Question:6

In the figure, LM is a line parallel to the y-axis at a distance of 3 units.
(i) What are the coordinates of the points P, R and Q?
(ii) What is the difference between the abscissa of the points L and M?

Answer:
(i) P = (3, 2)
R = (3, 0)
Q = (3, -1)
(ii) 0
Solution.
We have,

All the points lie on a line where the x coordinate is fixed, i.e., 3.
(i) Coordinate of the points P
Distance from x-axis: 2 units
So coordinates are (3, 2)
Coordinate of the points R
Distance from x-axis: 0 unit
So coordinates are (3, 0)
Coordinate of the points Q
Distance from x-axis: $-1unit$
So coordinates are (3, -1)
(ii) Abscissa is the x-axis (horizontal) coordinate
All the points lie on a line where the x coordinate is fixed, i.e., 3.
So the abscissa of L and M is the same, i.e., 3
Hence difference = 3 - 3 = 0

Question:7

In which quadrant or on which axis does each of the following points lie? (– 3, 5), (4, – 1), (2, 0), (2, 2), (– 3, – 6)

Answer:
(-3,5): 2nd Quadrant
(4, - 1): 4th Quadrant
(2, 0): x-axis
(2, 2): 1st Quadrant
(- 3, - 6): 3rd Quadrant
Solution.
Plotting the given points,(-3,5),(4,-1),(2,0),(2,2),(-3,-6)

Question:10

A point lies on the x-axis at a distance of 7 units from the y-axis. What are its coordinates? What will be the coordinates if it lies on the y-axis at a distance of $-7units$ from the x-axis?

Answer: (7,0)
Solution.
We know that the point that lies on the x-axis must have its y-coordinate as zero.
Here, it is given that a point lies on the x-axis at a distance of 7 units from the y-axis.
So y-coordinate = 0
The x-coordinate is the perpendicular distance from the y-axis, which is given as 7 units.
So, the x-coordinate is 7.
Hence coordinates are (7, 0)

Question:11

Find the coordinates of the point
(i) which lies on x and y axes both.
(ii) whose ordinate is -4 and which lies on the y-axis.
(iii) whose abscissa is 5 and which lies on the x-axis.

Answer:
(i) (0, 0)
(ii) (0, -4)
(iii) (5, 0)
Solution.
(i) We know that the point which lies on the x-axis and y-axis both is the origin whose coordinates are (0, 0)
(ii) We know that the point that lies on the y-axis must have its x-coordinate as zero.
Here, it is given that a point lies on the y-axis with ordinate -4
The ordinate is the y-axis (vertical) coordinate
So y-coordinate = -4
Hence coordinates are (0, -4)
(iii) We know that the point that lies on the x-axis must have its y-coordinate as zero.
Here, it is given that the point lies on the x-axis with abscissa 5
The abscissa is the x-axis (horizontal) coordinate
So x-coordinate = 5
Hence coordinates are (5, 0)
The points are shown as follows:

Question:12

Taking 0.5 cm as 1 unit, plot the following points on the graph paper:A (1,3), B(-3,-1), C(1,-4) ,D(-2,3) ,E(0,-8), F(1,0)

Answer:

$Scale0.5cm=1units$

Exercise: 3.4 Total Questions: 5 Page Numbers: 32

Question:1

Points A (5, 3), B (- 2, 3), and D (5, -4) are three vertices of a square ABCD. Plot these points on a graph paper and find the coordinates of the vertex C.

Answer: $(-2,-4)$
Solution.
Points $A(5,3),B(-2,3)$ and $D(5,-4)$ are three vertices of a square ABCD
If we plot them, we get:


Length of AD = Length of BC
Length of AB = Length of CD
From point D, we have made a parallel line to AB, towards the third quadrant.
Similarly, from point B, we have made a parallel line to AD, towards the third quadrant.
These lines intersect at the point $C(-2,-4).$
Hence, the square ABCD is formed, and C is $(-2,-4).$

Question:2

Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units, respectively, one vertex at the origin, the longer side lies on the x-axis, and one of the vertices lies in the third quadrant.

Answer:

Answer:
Coordinates of A (-5, 0)
Coordinates of B (-5, -3)
Coordinates of C (0, -3)
Coordinates of O (0, 0)
Solution.
Given rectangle has one vertex at the origin. Let the vertex be O.
∴ The coordinates of O are O (0, 0).
Let the rectangle be OABC.
Length = 5 units
Breadth = 3 units.
Now as the longer side is on the x-axis, we get that length lies on x-axis and breadth lies on the y axis.
So,
The coordinates of A are A (-5, 0)
The coordinates of C will be (0, -3).
Given that one of the vertex is in the third quadrant.
So, the rectangle lies in the III quadrant.
The coordinates of B will be (-5, -3).

Question:3

Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of point R such that PQRS is a square.

Answer: (4, 3)
Given
P (1, 0): Lies on the x-axis at a distance of 1 unit from the y-axis
Q (4, 0): Lies on the x-axis at a distance of 1 unit from the y-axis
Length of PQ = 4 -1 = 3 units
Let the coordinates of point R be (x, y)
Now, as PQRS is a square (PQ = QR = RS = SP)
Consider,
PQ = RS
3 = x - 1
So, x = 4
Similarly,
PQ = QR
3 = y - 0
So, y = 3
Hence, R is (4, 3)
The graph is as follows:

Question:5

Plot the points A (1, -1) and B (4, 5)
(i) Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points A and B.
(ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB.

Answer:

(i) (3, 3)
(ii) (5, 7)
Solution.
(i) Coordinates of a point on this line segment between the points A and B:C (3, 3), D (2.5, 2)

(ii) Coordinates of a point on this line which lies outside the line segment AB.E (5, 7), F (4.5, 6)

NCERT Exemplar Solutions Class 9 Maths Chapter 3 Important Topics:

NCERT exemplar Class 9 Maths solutions chapter 3 on Coordinate geometry deals with the following topics:

◊ Cartesian system: Any point in the plane is expressed.

◊ Coordinates of a point: An ordered pair to represent any point on the plane (X, Y).

◊ NCERT exemplar Class 9 Maths solutions chapter 3 includes physical interpretation of coordinates: Length of abscissa and ordinate.

◊ The possibility of coordinate: Different possibilities of coordinates in four parts of the plane.

◊ Horizontal axis and vertical axis: X-axis as the horizontal axis and Y-axis as the vertical axis.

◊ Importance of origin: The intersection point of two axes will be the reference point.

NCERT Class 9 Exemplar Solutions for other Subjects:

The following links will lead students to the solutions of other subjects' Exemplar solutions.

• NCERT Exemplar Class 9 Maths Solutions

• NCERT Exemplar Class 9 Science Solutions

Importance of NCERT Exemplar Class 9 Maths Solutions Chapter 3

These Class 9 Maths NCERT exemplar chapter 3 solutions will help the students grasp the basics of coordinate geometry and turn out to be extremely useful in higher Classes or competitive exams. Here are some of the important features of these solutions.

• Students will have a clear idea of how to draw coordinates on a graph paper when the coordinates are given.
• The concept of the Cartesian system and Quadrants will also become much clearer.
• Students will learn about shortcuts and alternative methods of solving these problems after checking these solutions.

NCERT Solution Subject Wise

Students can check the links below for the NCERT textbook solutions of other subjects.

• NCERT Solution for Class 9 Science
• NCERT Solution for Class 9 Maths

NCERT Notes Subject Wise

NCERT notes are a useful tool in the learning process. The following links are beneficial for that cause.

• NCERT Notes for Class 9 Science
• NCERT Notes for Class 9 Maths

NCERT Books and NCERT Syllabus

At the start of the preparation process, students should check the latest CBSE syllabus for changes and updates. They can use the links below to check the latest syllabus. Also, there are some reference books that students can use for further assistance.

• NCERT Syllabus Class 9 Maths
• NCERT Books Class 9
• NCERT Syllabus Class 9