NCERT Exemplar Class 9 Maths Solutions Chapter 3 Coordinate Geometry 2021

NCERT Exemplar Class 9 Maths Solutions Chapter 3 Coordinate Geometry

Edited By Safeer PP | Updated on Aug 31, 2022 11:40 AM IST

NCERT exemplar Class 9 Maths solutions chapter 3: Coordinate geometry is amongst the critical branches of maths and is used to draw any expression of a single variable on a plane. These NCERT exemplar Class 9 Maths chapter 3 solutions are a product of the considerable subject matter experts of our Mathematics team. These solutions are a good source to prepare for topics of NCERT Class 9 Maths. Due to their comprehensive details, these NCERT exemplar Class 9 Maths chapter 3 solutions cover the concepts of coordinate geometry to a large extent. NCERT exemplar Class 9 Maths solutions chapter 3 follows the CBSE 9 Class Syllabus covering all the topics recommended by the CBSE.

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Check the solutions of questions given in the book

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

Question:3

Point (0, –7) lies
(A) on the x –axis
(B) in the second quadrant
(C) on the y-axis
(D) in the fourth quadrant

Answer: [C] on the y-axis
Solution.
We know that
Coordinate of the x-axis is (x, 0) i.e., the value of y coordinate is zero
Coordinate of the y-axis is (0, y) i.e., the value of x coordinate is zero
So the point

(0, - 7)

is on the y-axis because here the value of x is 0 and value of y is 7.
Therefore option (C) is correct

Question:4

Point $(- 10, 0)$ lies
(A) on the negative direction of the x-axis
(B) on the negative direction of the y-axis
(C) in the third quadrant
(D) in the fourth quadrant

Answer: [A] on the negative direction of the x-axis
Solution.

Here the x-coordinate and y-coordinate is

- 10

and 0 respectively.
We know that coordinates on the negative direction of the x-axis is in the form

(- x, 0)

And the coordinates on the negative direction of the y-axis is in the form

(0, - y)

Hence point

(- 10, 0)

lies on the negative direction of the x-axis.
Therefore option (A) is correct

Question:5

Abscissa of all the points on the x-axis is
(A) 0
(B) 1
(C) 2
(D) any number

Answer: [D] any number
Solution.
We know that the coordinate of any point on the x-axis is (x, 0),
where x can take any value.
So, the abscissa of any point on the x axis is any number.
Therefore option (D) is correct

Question:6

Ordinate of all points on the x-axis is
(A) 0
(B) 1
(C) -1
(D) any number

Answer: [A]
Solution.
We know that the coordinate of every point on x-axis is (x, 0)
i.e., (7, 0), (1, 0) etc.
So the y-coordinate on the x-axis is always zero.
Hence the ordinate of every point on x-axis is 0.
Therefore option (A) 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 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 positive real number and - denotes the negative real number. So that we can say two coordinates are negative is 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 positive real number and - denotes the 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 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., y coordinate is zero on the x axis.
So if the y-coordinate of a point is zero, then this point always lies on 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 ofthe perpendicular lies on the negative direction of 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 y-coordinate of that point.
i.e., x coordinate is always perpendicular to y-axis.

(A) Here x-coordinate is -5. It lies on negative direction of x-axis so it is incorrect
(B) Here y-coordinate is 5. It lies on positive direction of y-axis and is perpendicular to x-axis so it is incorrect
(C) Here y-coordinate is -5. It lies on negative direction of y-axis and is perpendicular to x-axis.
So it is incorrect
(D) Here y-coordinate is 5 or -5, i.e., perpendicular distance can be in 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 figure is obtained?
(A) Square
(B) Rectangle
(C)Trapezium
(D) Rhombus

Answer: (B) Rectangle
Solution.

(C)Rectangle: We know that in the rectangle opposite side 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:15

If the coordinates of the two points are P(-2,3) and Q(-3, 5), then (abscissa of P) - (abscissa of Q) is:
(A) -5
(B) 1
(C) -1
(D) -2

Answer: (B) 1
Solution.

The coordinates of the two points are P(-2,3) and Q(-3, 5).
The abscissa is the x-axis (horizontal) coordinate
The abscissa of P - abscissa of Q
-2-(-3)
=1
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) Point R and S lie on 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, y coordinate is always zero. So it is incorrect.
(D) Point Q and O have 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 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:18

The points whose abscissa and ordinate have different signs will lie in
(A) I and II quadrants
(B) II and III quadrants
(C) I and III quadrants
(D) II and IV quadrants

Answer: (D) II and IV quadrants
Solution.
The abscissa is the x-axis (horizontal) coordinate
The ordinate is the y-axis (vertical) coordinate
We know that
The sign of coordinates in the first quadrant is (+, +)
The sign of coordinates in the second quadrant is (–, +)
The sign of coordinates in the third quadrant is (–, –)
The sign of coordinates in the fourth quadrant is (+, –)
So that we can say that in II and III quadrant abscissa and ordinate are having different signs.
Therefore option (D) 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 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

Question:21

The point whose ordinate is 4 and which lies on y-axis is
(A) (4, 0)
(B) (0, 4)
(C) (1, 4)
(D) (4, 2)

Answer: (B) (0, 4)
Solution.
The ordinate is the y-axis (vertical) coordinate
(A) (4, 0) is lying on x-axis because here abscissa is 4 and ordinate is 0.
(B) (0, 4) is lying on y-axis because here abscissa is 0 and ordinate is 4
(C) (1, 4) lies in I quadrant because here abscissa is 1 and ordinate is 4
(D) (4, 2) lies in I quadrant because here abscissa is 4 and ordinate is 2
Therefore option (B) is correct

Question:22

Which of the points P(0. 3), Q(1, 0), R(0, -1), S(-5, 0), T(1, 2) do not lie on the x-axis?
(A) P and R only
(B) Q and S only
(C) P, R and T
(D) Q, S and T

Answer: (C) P, R and T
Solution.
We know that points on x axis have coordinates (x, 0). Points on y axis have coordinates (0, y). So, that we can say Q(1, 0), S(-5, 0) lies on x-axis
and P(0, 3), R(0, -1) lies on the y-axis and T(1, 2) lies in the I quadrant. Hence P, R and T do not lie on the x-axis.
Therefore option (C) is correct

Question:23

The point which lies on y-axis at a distance of 5 units in the negative direction of y-axis is
(A) (0, 5)
(B) (5, 0)
(C) (0,-5)
(D) (-5,0)

Answer: (C)

(0, - 5)

Solution.
We know that the point lies on y-axis so its x-coordinate is zero.
Also, it is a distance of 5 units in the negative direction of y-axis.
So that y-coordinate is negative with an ordinate of 5.
(A) (0, 5) lies in the positive direction in y-axis.
(B) (5, 0) lies on positive direction in x-axis.
(C)

(0, - 5)

lies in the negative direction in y-axis.
(D)

(- 5, 0)

lies in the negative direction in x-axis.
Therefore option (C) is correct

Question:24

The perpendicular distance of the point P (3, 4) from the y-axis is
(A) 3
(B) 4
(C) 5
(D) 7

Answer: [A] 3
Solution.
Plotting the point (3, 4) on the graph:
We know that the perpendicular distance from y-axis is the x-coordinate (abscissa).
So here 3 is the perpendicular distance from the y-axis and 4 is the perpendicular distance from x-axis.
Hence 3 is the correct answer.
Therefore option (A) is correct

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 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:3

Write whether the following statements are True or False? Justify your answer. The coordinates of a point whose ordinate is -1/2 and abscissa is 1 are -1/2 , 1.

Answer: False
The abscissa is the x-axis (horizontal) coordinate
The ordinate is the y-axis (vertical) coordinate
Here ordinate is -1/2 and abscissa is 1.
So the coordinates are (1, -1/2) and not (-1/2, 1) .
Therefore the given statement is False.

Question:4

Write whether the following statements are True or False? Justify your answer. A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0).

Answer: False
Solution.
We know that points that lie on the y-axis have coordinate in the form (0, y).
So we can say that x-coordinate should be zero.
The distance from x-axis will be equal to its y-coordinate.
So the point will be (0, 2)
But here the point is given as (2, 0) so the 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., x-coordinate is negative and y-coordinate is positive.
Therefore the given statement is True.

Question:1

Write the coordinates of each of the points P, Q, R, S, T and O from the Figure.

Answer:

Coordinates of any point are in the form (x, y).
From the given graph, we can see:
Coordinate of point P=(1, 1)
Coordinate of point Q=(-3, 0)
Coordinate of point R = (-2, -3)
Coordinate of point S = (2, 1)
Coordinate of point T = (4, -2)
Coordinate of point O = (0, 0)

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:3

Plot the points (x, y) given by the following table

Answer:

The given points can be plotted as follows:

Question:1

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:2

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:3

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 col linear

Question:5

Without plotting the points indicate the quadrant in which they will 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

Answer:
(i) II quadrant
(ii) III quadrant
(iii) II quadrant
(iv) I quadrant
Solution.
We know that sign in I quadrant = (+, +)
In II quadrant = (-, +)
In III quadrant = (-,-)
In IV quadrant = (+,-)
Abscissa is the x-axis (horizontal) coordinate
Ordinate is the y-axis (vertical) coordinate
(i) Hence abscissa is -3 and ordinate is 5.
So, it lies in II quadrant.
(ii) Here x coordinate is -5 and y-coordinate is -3
So both are negative.
Its lies in III quadrant.
(iii) Abscissa is -5 and ordinate is 3
Here x coordinate is -5 and y-coordinate is 3
So it lies in II quadrant.
(iv) Ordinate is 5 and abscissa is 3
Here x coordinate is 3 and y-coordinate is 5
Both are positive.
So it lies in I quadrant

Question:6

In 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 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:

- 1 u n i t

So coordinates are (3, -1)
(ii) Abscissa is the x-axis (horizontal) coordinate
All the points lie on a line where x coordinate is fixed, i.e., 3.
So 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 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:8

Which of the following points lie on y-axis ?
A (1, 1), B (1, 0), C (0, 1), D (0, 0), E (0, - 1), F (- 1, 0), G (0, 5), H (- 7, 0), I (3, 3).

Answer:

C(0, 1), D (0, 0), E(0, -1), G(0, 5)

Solution.
We know that for points that lie on the y-axis, x coordinate should be zero. The abscissa is the x-axis (horizontal) coordinate, which should be zero.

Question:9

Plot the points (x, y) given by the following table. Use scale 1 cm = 0.25 units

Answer:

Scale 1 cm = 0.25 units
The points are as follows:
(1.25, -0.5) = (5 units, -2 units)
(0.25, 1) = (1 unit, 4 units)
(1.5, 1.5) = (6 units, 6 units)
(-1.75, -0.25) = (-7 units, -1 unit)
The graph will be as follows:

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 y-axis at a distance of $- 7 u n i t s$ from x-axis ?

Answer: (7,0)
Solution.
We know that the point that lies on 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
x-coordinate is the perpendicular distance from the y-axis which is given as 7 units
So, 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 y-axis.
(iii) whose abscissa is 5 and which lies on x-axis.

Answer:
(i) (0, 0)
(ii) (0, -4)
(iii) (5, 0)
Solution.
(i) We know that the point which lies on x-axis and y-axis both is origin whose coordinates are (0, 0)
(ii) We know that the point that lies on 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 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:

S c a l e 0.5 c m = 1 u n i t s

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 hence 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 the point R such that PQRS is a square.

Answer: (4, 3)
Given
P (1, 0): Lies on x-axis at a distance of 1 unit from y-axis
Q (4, 0): Lies on x-axis at a distance of 1 unit from y-axis
Length of PQ = 4 -1 = 3 units
Let 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:4

From the Fig. 3.8, answer the following:
(i) Write the points whose abscissa is 0.
(ii) Write the points whose ordinate is 0.
(iii) Write the points whose abscissa is -5.

Answer:
(i) A (0, 3); L (0, -4)
(ii) G (5, 0); I (-2, 0)
(iii) D (-5, 1); H (-5, -3)
Abscissa is the x-axis (horizontal) coordinate
Ordinate is the y-axis (vertical) coordinate
(i) Abscissa is given as 0
So, x-coordinate must be zero.
Hence points are A (0, 3); L (0, -4)
(ii) Ordinate is given as 0
So, y-coordinate must be zero.
Hence points are G (5, 0); I (-2, 0)
(iii) Abscissa is given as -5
So, x-coordinate must be -5.
Hence points are D (-5, 1); H (-5, -3)

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 include 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 which will be the reference point.

NCERT Class 9 Exemplar Solutions for Other Subjects:

NCERT Class 9 Maths Exemplar Solutions for Other Chapters:

Chapter 1 Number System

Chapter 2 Polynomials

Chapter 4 Linear equations in Two Variable

Chapter 5 Introduction to Euclid’s Geometry

Chapter 6 Lines and Angles

Chapter 7 Triangles

Chapter 8 Quadrilaterals

Chapter 9 Area of Parallelograms and Triangles

Chapter 10 Circles

Chapter 11 Constructions

Chapter 12 Heron’s Formula

Chapter 13 Surface Areas and Volumes

Chapter 14 Statistics and Probability

Features 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.
The student will learn to draw any expression on a plane by dividing the plane into four parts by two perpendicular lines known as X-axis and Y-axis(Y coordinate can be treated as the value of expression for different values of X coordinate).
The Class 9 Maths NCERT exemplar solutions chapter 3 Coordinate Geometry is appropriate to attempt the questions of other books such as NCERT Class 9 Maths, RD Sharma Class 9 Maths or RS Aggarwal Class 9 Maths.

NCERT exemplar Class 9 Maths solutions chapter 3 pdf download is an interesting feature which permits the students to view/download these solutions of NCERT exemplar Class 9 Maths chapter 3 and practice from them in an offline mode.

Check the solutions of questions given in the book

Chapter No.	Chapter Name
Chapter 1	Number Systems
Chapter 2	Polynomials
Chapter 3	Coordinate Geometry
Chapter 4	Linear Equations In Two Variables
Chapter 5	Introduction to Euclid's Geometry
Chapter 6	Lines And Angles
Chapter 7	Triangles
Chapter 8	Quadrilaterals
Chapter 9	Areas of Parallelograms and Triangles
Chapter 10	Circles
Chapter 11	Constructions
Chapter 12	Heron’s Formula
Chapter 13	Surface Area and Volumes
Chapter 14	Statistics
Chapter 15	Probability

Also, Read NCERT Solution Subject Wise

Check NCERT Notes Subject Wise

Also Check NCERT Books and NCERT Syllabus here

Frequently Asked Questions (FAQs)

1. Can we draw any expression of a single variable on the Cartesian plane?

Yes, we can draw any expression of a single variable on the Cartesian plane. The same can be done by tabular form data of a variable and the value of expression.

2. Can we draw the expression of two variables on the Cartesian plane?

No, we cannot draw an expression of two variables, in such a case, we need to locate

three things: two variables and the value of expression.

3. Can we solve zeros of any polynomial with the help of Coordinate geometry?

Yes, we can solve the zeros of any polynomial. The computers solve polynomial zeros with the help of Coordinate Geometry, which cannot be solved algebraically.

4. The chapter on coordinate geometry constitutes for how many marks in the final examination?

Generally, 5-7% of the weightage of the whole paper is given to the questions of Coordinate Geometry. These NCERT Exemplar Class 9 Maths solutions chapter 3 provides the detailed solutions so that the students can understand and score well in the examination.

5. What is the weightage of Coordinate Geometry for exams like IITJEE Advanced?

It is one of the essential branches of mathematics which is asked in IIT, JEE Advanced for several years and ranges up to 17% of the whole paper.

Also Read

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NCERT Class 9 Maths Chapter 5 Notes Introduction To Euclid’s Geometry - Download PDF

NCERT Class 9 Maths Chapter 6 Notes Lines and Angles - Download PDF

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

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NCERT Exemplar Class 9 Maths Solutions Chapter 3 Coordinate Geometry

NCERT Exemplar Solutions Class 9 Maths Chapter 3 Important Topics:

NCERT Class 9 Exemplar Solutions for Other Subjects:

NCERT Class 9 Maths Exemplar Solutions for Other Chapters:

Features of NCERT Exemplar Class 9 Maths Solutions Chapter 3:

Check the solutions of questions given in the book

Also, Read NCERT Solution Subject Wise

Check NCERT Notes Subject Wise

Also Check NCERT Books and NCERT Syllabus here

Frequently Asked Questions (FAQs)

Also Read

Articles

Upcoming School Exams

Andhra Pradesh Residential Junior Colleges Common Entrance Test

Telangana Residential Junior Colleges Common Entrance Test

Chattisgarh State Open School 12th Examination

Chattisgarh State Open School 10th Examination

Punjab Board of Secondary Education 12th Examination