Lesson: Coordinate Geometry

Exercise 3.1 (24 Multiple choice Questions and

answers)

Question: 1

Point (–3, 5) lies in the:

(a) first quadrant

(b) second quadrant

(d) fourth quadrant

Solution:

The x-coordinate of the point (-3, 5) is negative and

the sign of the y-coordinate is positive, so, it lies in the

second quadrant.

Question: 2

Which of the following option shows the signs of the

abscissa and ordinate of a point in the second

quadrant?

(a) (+, +)

(b) (–, –)

(d) (+, –)

Solution:

Question: 3

Point (0, –7) lies:

(a) on the x –axis.

(b) in the second quadrant.

(d) in the fourth quadrant.

Solution:

The x - coordinate of the point (0, −7) is 0. Therefore,

it the y – axis.

Question: 4

Point (– 10, 0) lies:

(a) on the negative direction of the x-axis.

(b) on the negative direction of the y-axis.

(d) in the fourth quadrant.

Solution:

The x - coordinate of the point (−10, 0) is negative

and the y - coordinate is 0.So, it lies on the negative

direction of the x - axis.

Question: 5

Abscissa of all the points on the x-axis is:

(a) 0

(b) 1

(d) any number

Solution:

Abscissa of all the points on the x-axis can be any

number.

Question: 6

Ordinate of all points on the x-axis is:

(a) 0

(b) 1

(d) Any number

Solution:

On the x-axis, ordinate of all the points is 0.

Question: 7

The point at which the two coordinate axes meet is

called the:

(a) abscissa

(b) ordinate

(d) quadrant

Solution:

The point at which the two coordinate axes meet is

called the origin.

Question: 8

A point both of whose coordinates are negative will lie

in:

(a) I quadrant

(b) II quadrant

(d) IV quadrant

Solution:

In the third quadrant, the coordinates of all the points

will be negative. Hence, 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

(d) do not lie in the same quadrant

Solution:

The point (1, −1), (2, −2), and (4, −5) lie in the

quadrant. The point (−3, −4), lie in III quadrant.

Hence, 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

(d) on y – axis

Solution:

The y-coordinate of all the points on the x–axis is

always zero. Hence, 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

(d) IV and II quadrants, respectively

Solution:

The y-coordinate of the point

(–5, 2) is negative and

the coordinate is positive.

Hence, it lies in the II quadrant.

The x-coordinate of the point

(2, –5) is positive and

the y-coordinate is negative.

Hence, it 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 x – axis, then the point P

has

(a) x-coordinate = − 5

(b) y -coordinate = − 5 only

(d) y-coordinate = 5 or − 5

Solution:

Since, 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

x - axis, then the point P can lie either on the II

quadrant or the III quadrant. Hence, the

y - coordinate can be either 5 or −5.

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 one of the

following figures is obtained?

(a) Square

(b) Rectangle

(d) Rhombus

Solution:

Here, the point O(0, 0), is the origin. The point

A(3, 0) lies on the positive direction of the x - axis, the

point B(3, 4),lies in the first quadrant and the point

C(0, 4), lies on the positive direction of y - axis. On

joining OA, AB, BC and CO, the figure obtained 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 a graph paper, then the point

(s) in the fourth quadrant are:

(a) R and T

(b) Q and R

(d) P and R

Solution:

The x-coordinate of the point P(−1, 1) is −1 and the y

- coordinate is 1.

So, it lies in the 2

quadrant.

Similarly, we can plot all the points;

Q(3, −4), R(1, −1), S(−2, −3) and T(−4, 4).

It is clear from the graph that the points and lie in the

fourth quadrant.

Question: 15

If the coordinates of two points are P(−2, 3) and

Q(−3, 5), then (abscissa of P) −(abscissa of Q) is:

(a) −5

(b) 1

(d) −2

Solution:

Abscissa of the point P is −2 and for the point Q

is −3.

Hence, (abscissa of P) – (abscissa of Q)

= (−2) − (−3)

= − 2 + 3

= 1

Question: 16

If P(5, 1), Q(8, 0), R(0, 4), S(0, 5), and O(0, 0), are

plotted on a graph paper, then the point (s) on the

x - axis are:

(a) P and R

(b) R and S

(d) Q and O

Solution:

A point lies on the x-axis, if its y-coordinate is zero.

Hence, on plotting the given points on a graph paper,

we can see that Q and O lie on the x-axis.

Question: 17

Abscissa of a point is positive in:

(a) I and II quadrants

(b) I and IV quadrants

(d) II quadrant only

Solution:

Abscissa of any point in the I quadrant or the IV

quadrant is always positive. Hence, 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

(d) II and IV quadrants

Solution:

In the I quadrant, the abscissa and the ordinate of any

point are positive.

In the II quadrant, the abscissa of any point is negative

and the ordinate is positive.

In the III quadrant, the abscissa of any point is

negative and the ordinate is also negative.

In the IV quadrant, the abscissa of any point is

positive and the ordinate is negative.

Hence, option (d) is correct.

Question: 19

In the given figure, coordinates of P are:

(a) (−4, 2)

(b) (−2, 4)

(d) (2, −4)

Solution:

The perpendicular distance of the point P is 2 units

from y - axis. So, the value of the x - coordinate will

be −2.

Also, the perpendicular distance of the point from the

x-axis is 4 units. So, the value of the

y- coordinate will be 4.

Therefore, the coordinates of the point P will be.

Question: 20

In the following figure, the point identified by the

coordinates (–5, 3) is:

(a) T

(b) R

(d) S

Solution:

Question: 21

The point whose ordinate is and which lies on

y - axis is:

(a) (4, 0)

(b) (0, 4)

(d) (4, 2)

Solution:

Since, the point lies on y – axis, the x - coordinate will

be 0.Also, the ordinate or value of y - coordinate is 4.

Therefore, the coordinates of the point will be

(0, 4).

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 P only

(b) Q and S only

(d) Q, S and T

Solution:

The y - coordinate will be zero for all the points that

lie on x - axis. The points P,R and T have

y – coordinate value greater than zero. Hence, these

points do not lie on the x - axis.

Question: 23

The point which lies on y - axis at a distance of

5 units, in the negative direction from x - axis is 5:

(a) (0, 5)

(b) (5, 0)

(d) (−5, 0)

Solution:

Since, the point lies on the y - axis, the x - coordinate

will be zero. Also, this point lies on the y - axis at a

distance of 5 units, in the negative direction of

y - axis.

Hence, the y - coordinate will be −5.

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

(d) 7

Solution:

The perpendicular distance of the point P (3, 4) from

the y-axis is 3.

Exercise 3.2

Question: 1

Write whether the following statements are

True or False? Justify your answer.

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

(ii) Point (1, −1) and (1, −1) lies in the first quadrant.

(iii) The coordinates of a point whose ordinate is and

abscissa is 1 are

(iv) A point lies on y - axis at a distance of 2 units

from the x - axis. Its coordinates are (2, 0).

(v) (3, 0) is a point in the quadrant.

Write whether the following statements are True or

False? Justify your answer.

Solution:

(i) False, because if the ordinate of a point is zero, the

point lies on the x-axis.

(ii) False.

(1, –1 ) lies in the IV quadrant and (–1, 1) lies in the II

quadrant.

(iii) False, because in the coordinates of a point, the

abscissa is written first and then the ordinate.

(iv) False, because a point on the y-axis is of the form

(0, y).

(v) True, because in the II quadrant, the signs of the

abscissa and the ordinate are – and + respectively.

Exercise 3.3

Question: 1

Write the coordinates of each of the points P, Q, R, S,

T and O from the given below figure.

Solution:

Here, the points P and S lie in the quadrant. So, their

coordinates will be positive.

Now,

the perpendicular distance of P from both axes is1.

Therefore, the coordinates of Pare (1, 1).

The perpendicular distance of S from the x - axis

is 1 unit and from the y - axis is 2 units. So, the

coordinates of are (2, 1).

The point Q lies on the x - axis in the negative

direction. So, its y – coordinate is zero and

x - coordinate is −3.

So, the coordinates of Q are (−3, 0).

The point R lies in the III quadrant.

Hence, both coordinates will be negative.

Now, its perpendicular distance from the x - axis is 3

units and from the y - axis is 2 units. So, the

x - coordinates of the point R are (−2, −3).

The point lies in the III quadrant.

Hence, both coordinates will be negative.

Now, its perpendicular distance from the x - axis is 2

units and from the y - axis is 4 units. So, the

coordinates of T are (4, −2).

The point O is the intersection of both the axes. So, it

is the origin and its coordinates are 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)

Solution:

Let X’OX and Y’OY be the coordinate axes and lets

mark points on it. Here point P(3, 2) lies in the II

quadrant,

Q(–7, –3) lies in the III quadrant, R( 6, -3) lies in the

IV quadrant and S(2, 2) lies in the I quadrant. Plotting

these points on the graph paper, the figure obtained is

the trapezium PQRS.

Question: 3

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

3

2

3

Solution:

On plotting the given points on a graph paper, we get

the points P(2, 4), Q(4,2) R(-3, 0), S(-2, 5), T(3, -3)

and O(0, 0) as shown in the graph.

Question: 4

Plot the following points and check whether they are

collinear or not:

(i) (1, 3), (– 1, – 1), (– 2, – 3)

(ii) (1, 1), (2, – 3), (– 1, – 2)

(iii) (0, 0), (2, 2), (5, 5)

Solution:

(i) Plotting the points P(1,3) , Q(–1, –1) and R (–2, –3)

on a graph paper and joining these points, we get a

straight line. Hence, these points are collinear.

(ii) Plotting the points P(1, 1), Q(2, –3) and R (–1, –2)

on a graph paper and joining these points, we get three

lines i.e., the given points do not lie on the same line.

Therefore, the given points are not collinear.

(iii) Plotting the points O(0, 0) , A(2, 2) and B (5,5) on

a graph paper and joining these points, we get a

straight line. Hence, the given points are collinear.

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

Solution:

(i) The given point is (–3, 5). Here, the abscissa is

negative and ordinate is positive. Therefore, it lies in

II quadrant.

(ii) The given point is (–5, –3). Here, both the abscissa

and the ordinate are negative. Therefore, it lies in the

III quadrant.

(iii) The given point is (–5, 3). Here, the abscissa is

negative and the ordinate is positive. Therefore, it lies

in the II quadrant.

(iv) The given point is (3, 5). Here, both the abscissa

and the ordinate are positive. Therefore, it lies in the I

quadrant.

Question: 6

In the given 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?

Solution:

Given LM is a line parallel to the y-axis and its

perpendicular distance from y axis is 3 units.

(i)The coordinates of the point P= (3, 2) [Since, its

perpendicular distance from the x- axis is 2 units] The

coordinate of the point Q= (3, –1) [Since, its

perpendicular distance from the x- axis is 1 unit and in

the negative direction of y-axis].

The coordinates of point R= (3, 0) [Since, it lies on the

x-axis, its y-coordinate is zero].

(ii) The abscissa of the point L= 3 and the abscissa of

the point M=3

The difference between the abscissas of the points L

and M = 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)

Solution:

(i) The x-coordinate of the point (-3, 5) is negative and

the y-coordinate is positive. Therefore, it lies

in the II quadrant.

(ii) The x-coordinate of the point (4, -1) is positive and

the y-coordinate is negative. Therefore, it lies

in the IV quadrant.

(iii) The x-coordinate of the point (2, 0) is positive and

the y-coordinate is zero. So, it lies on the x-axis.

(iv) The x-coordinate and the y-coordinate of the point

(2, 2) are positive. So, it lies in the I quadrant.

(v) The x-coordinate and the y-coordinate of the point

(-3, -6) are negative. So, it lies in the III quadrant.

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).

Solution:

A point lies on the y-axis, if its x-coordinate is zero.

Here, x coordinates of the points C(0, 1), D(0, 0), E(0,

-1) and G(0, 5) are zero. So, these points lie on the y-

axis.

Also, D(0, 0) is the intersection point of both the axes.

So it lies on the y- axis as well as on the x- axis.

Question: 9

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

scale 1 cm = 0.25 units:

1.25

0.25

1.5

1.75

-0.5

1.5

0.25

Solution:

Let X’OX and Y’OY be the coordinate axes.

Let’s plot the given points (1.25, -0.5), (0.25, 1), (1.5,

1.5) and

(–1.75, – 0.25) on a graph paper. After plotting, we get

the points P (1.25, –0.5), Q(0.25, 1), R(1.5, 1.5) and

S(–1.75, –0.25).

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 units

from x-axis?

Solution:

The given point lies on the positive direction of x-axis.

So, its y-coordinate will be zero. It is at a distance of 7

units from the y-axis. So, its coordinates are (7, 0).

If it lies on the negative direction of y-axis, then its x-

coordinate will be zero. Its distance from x-axis is 7

units. Its coordinates are (0, –7).

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.

Solution:

(i) The point which lies on the x and the y-axis both is

the origin whose coordinates are (0, 0).

(ii) The point whose ordinate is –4 and which lies on

y-axis, i.e., whose x-coordinate is zero, is (0, –4).

(iii) The point whose abscissa is 5 and which lies on x-

axis, i.e., whose y-coordinate is zero, is (5, 0).

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)

Solution:

The x and y–coordinates of the point A(1, 3) are

positive. Therefore, it lies in the I quadrant.

The x and y–coordinates of point B(–3, –1) are

negative. Therefore, it lies in III quadrant.

The x-coordinate of the point C(1, –4) is positive and

the y-coordinative is negative.

Therefore, it lies in the IV quadrant.

The x-coordinate of the point D(–2, 3) is negative and

the y-coordinate is positive. So, it lies in the II

quadrant.

The x-coordinate of the point E( 0, –8 ) is zero.

Therefore, it lies on the y-axis.

The x and the y-coordinate of the point F(1, 0) is zero.

So, it lies on the x-axis.

On plotting the given points, we can draw follwing

graph.

Exercise 3.4

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.

Solution:

The graph obtained by plotting the points A, B and D

is given below.We take a point C on the graph such

that ABCD is a square i.e., all sides AB, BC, CD and

AD are equal.

So, the abscissa of C should be equal to the abscissa of

B i.e., –2, and the ordinate of C should be equal to the

ordinate of D i.e., –4.

Hence, the coordinates of C are (–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.

Solution:

Given length of a rectangle = 5 units

Given breadth of a rectangle = 3 units

One vertex is at origin i.e., D(0, 0) and one of the

other vertices lies in the III quadrant.

The length of the rectangle is 5 units in the negative

direction of the x–axis.

The vertex of A is (–5, 0). Also, the breadth of the

rectangle is 3 units in the negative direction of the y-

axis. The vertex of C is (0, –3). The fourth vertex B is

(–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.

Solution:

The y-coordinate of the point P(1, 0) is zero.

Therefore, it lies on the x-axis .

The y- coordinate of the point Q(4, 0) is zero.

Therefore, it lies on the x-axis.

Both coordinates of the point S(1, 3) are positive.

Therefore, it lies on the I quadrant.

On plotting these points, we get the

Graph as shown.

Now, let’s take a point R on the graph such that PQRS

is a square. Then, all

sides will be equal i.e., PQ = QR = RS = PS.

So, the abscissa of R should be equal to

the abscissa of Q i.e., 4 and the ordinate of R should

be equal to the ordinate of S i.e., 3.

Hence, the coordinates of R are (4, 3).

Question: 4

From the given figure, 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.

Solution:

(i) The point whose abscissa is 0 will always lie on the

y-axis. So, the required points whose abscissa is 0 are

A, L and O.

(ii) The point whose ordinate is 0 will always lie on

the x-axis. So, the required points whose ordinate is 0

are G, I and O.

(iii) Here, the abscissa ‘– 5’ is negative. The points

with abscissa –5 will lie in II and III quadrants. So, the

required points whose abscissa is –5, are D and H.

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.

Solution:

In the point A(1, –1), the x-coordinate is positive and

the y-coordinative is negative. So, it lies in the IV

quadrant.

In the point B(4, 5), both the coordinates are positive.

So, it lies in the I quadrant.

On plotting these point, we get the graph as shown.

(i) On joining the points A and B, we get the line

segment AB.

Now, to find the coordinates of a point on this line

segment between A and B, we draw a perpendicular

line to the x – axis from x = 2.

Since, x = 2 lies between A and B, it intersect the line

segment AB at S. Now, we draw a perpendicular from

S to the y–axis such that it intersects the y–axis at y =

1. Thus, we get a point (2, 1) which lie on the line

segment AB.

(ii) Now, we extend the line segment AB such that it

intersects the y-axis at point Q. Thus, we get

the point Q(0, – 3) which lies outside the line segment

AB.