myhelper: RD Sharma 2020 solution class 9 chapter 8 Coordinate Geometry MCQS

MCQS

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Question 1:

Mark the correct alternative in each of the following:

The point of intersect of the coordinate axes is

(a) ordinate

(b) abscissa

(c) quadrant

(d) origin

Answer 1:

As we know that:

The distance of a point from y−axis is called its x−coordinate or abscissa.

The distance of a point from x−axis is called its y−coordinate or ordinate.

The coordinate axes divide the plane into four equal parts which are known as quadrants.

The point of intersection of the coordinate axes is called the origin and the coordinates of origin are.

Example is shown in the graph

Thus the correct answer is (d).

Question 2:

The abscissa and ordinate of the origin are

(a) (0, 0)

(b) (1, 0)

(c) (0, 1)

(d) (1, 1)

Answer 2:

As we know that:

The distance of a point from y−axis is called its x−coordinate or abscissa.

The distance of a point from x−axis is called its y−coordinate or ordinate.

The coordinate axes divide the plane into four equal parts which are known as quadrants.

The point of intersection of the coordinate axes is called the origin and the coordinates of origin are.

The origin is shown in the graph

Thus the correct answer is (a).

Question 3:

The measure of the angle between the coordinate axes is

(a) 0°

(b) 90°

(c) 180°

(d) 360°

Answer 3:

As we know that x−axis and y−axis intersect to each other at point O and perpendicular to each other. So, the angle between the coordinate axes is.

Thus the correct answer is (b).

Question 4:

A point whose abscissa and ordinate are 2 and −5 respectively, lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

Answer 4:

As shown in graph that a point whose abscissa and ordinate areand respectively lies in the fourth quadrant.

Thus the correct answer is (d).

Question 5:

Points (−4, 0) and (7, 0) lie

(a) on x-axis

(b) y-axis

(c) in first quadrant

(d) In second quadrant

Answer 5:

Let the points P and Q whose coordinates are andrespectively. Locate the points and you will see that they lie on x-axis.

Thus the correct answer is (a).

Question 6:

The ordinate of any point on x-axis is

(a) 0

(b) 1

(c) −1

(d) any number

Answer 6:

We know that the y−coordinates of every point on x−axis are zero. So, the coordinates of any point on the x−axis are of the form.

Thus the correct answer is (a).

Question 7:

The abscissa of any point on y-axis is

(a) 0

(b) 1

(c) −1

(d) any number

Answer 7:

We know that the x−coordinate of every point on y-axis is zero. So, the coordinates of any point on the x−axis are of the form.

Thus the correct answer is (a).

Question 8:

The abscissa of a point is positive in the

(a) First and Second quadrant

(b) Second and Third quadrant

(c) Third and Fourth quadrant

(d) Fourth and First quadrant

Answer 8:

The signs of coordinates of a point in various quadrants are shown in the following graph:

Thus the correct answer is (d).

Question 9:

A point whose abscissa is −3 and ordinate 2 lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

Answer 9:

As we know that

In the first quadrant

In the second quadrant

In the third quadrant

In the fourth quadrant

The point whose abscissa is −3 which is negative and ordinate 2 is positive, so this point lies in the second quadrant.

Thus the correct answer is (b).

Question 10:

Two points having same abscissae but different ordinate lie on

(a) x-axis

(b) y-axis

(c) a line parallel to y-axis

(d) a line parallel to x-axis

Answer 10:

Let the points and having the same abscissa but different ordinates be shown in the graph given below:

Fig: (location of two considered points)

And these points lie on a line parallel to y−axis

Thus the correct answer is (c).

Question 11:

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

(a) 4

(b) 3

(c) 5

(d) none of these

Answer 11:

The point is shown in the graph given below:

Thus the perpendicular distance of the point from x−axis is 3 units.

Thus the correct answer is (b).

Question 12:

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

(a) 4

(b) 3

(c) 5

(d) none of these

Answer 12:

The point is shown in the graph given below:

Thus the perpendicular distance of the point from y−axis is 4.

Thus the correct answer is (a).

Question 13:

The points (other than origin) for which abscissa is equal to the ordinate will lie in
(a) I quadrant only
(b) I and II quadrants
(c) I and III quadrants
(d) II and IV quadrants

Answer 13:

In I quadrant: x > 0, y > 0

In II quadrant: x < 0, y > 0

In III quadrant: x < 0, y < 0

In IV quadrant: x > 0, y < 0

The points for which abscissa is equal to the ordinate, both x and y must be of same sign i.e. either x > 0, y > 0 or x < 0, y < 0.

The co-ordinates of the points for which abscissa is equal to the ordinate are of the form (x, y) or (−x, −y), where x = y.

Thus, the points (other than origin) for which abscissa is equal to the ordinate will lie in I and III quadrants.

Hence, the correct answer is option (c).

Question 14:

Signs of the abscissa and ordinate of a point in the second quadrant are respectively
(a) +, +
(b) –, –
(c) –, +
(d) +, –

Answer 14:

In the second quadrant, x < 0, y > 0.

Thus, the signs of the abscissa and ordinate of a point in the second quadrant are negative and positive, respectively. That is, x is − and y is +.

Hence, the correct answer is option (c).

Question 15:

Abscissa of all points on the x-axis is
(a) 0
(b) 1
(c) 2
(d) any number

Answer 15:

Disclaimer: The answer has been provided for the following question.

Ordinate of all points on the x-axis is
(a) 0
(b) 1
(c) 2
(d) any number

Solution:

If we take any point on the x-axis, then the distance of this point from the x-axis is 0. Therefore, the ordinate of this point is 0.

The co-ordinate of a point on the x-axis are of the form (x, 0). So, the ordinate of all points on the x-axis is 0.

Hence, the correct answer is option (a).

Question 16:

Ordinate of all points on the y-axis is
(a) 0
(b) 1
(c) 2
(d) any number

Answer 16:

Disclaimer: The answer has been provided for the following question.

Abscissa of all points on the y-axis is
(a) 0
(b) 1
(c) 2
(d) any number

Solution:

If we take any point on the y-axis, then the distance of this point from the y-axis is 0. Therefore, the abscissa of this point is 0.

The co-ordinate of a point on the y-axis are of the form (0, y). So, the abscissa of all points on the y-axis is 0.

Hence, the correct answer is option (a).

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Question 17:

A point whose abscissa and ordinate both are negative will lie in
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant

Answer 17:

In the third quadrant, x < 0, y < 0. Thus, the point whose abscissa and ordinate both are negative will lie in III quadrant.

Hence, the correct answer is option (c).

Question 18:

Points (2, –2), (3, –3), (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 18:

The given points are (2, –2), (3, –3), (4, –5) and (–3, –4).

In the third quadrant: x < 0, y < 0

So, the point (–3, –4) lie in the III quadrant.

In the fourth quadrant: x > 0, y < 0

So, the points (2, –2), (3, –3), (4, –5) lie in the IV quadrant.

Thus, the given points (2, –2), (3, –3), (4, –5), (–3, –4) do not lie in the same quadrant.

Hence, the correct answer is option (d).

Question 19:

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 19:

In I quadrant: x > 0, y > 0

In II quadrant: x < 0, y > 0

In III quadrant: x < 0, y < 0

In IV quadrant: x > 0, y < 0

The abscissa and ordinate have the same sign in I and III quadrants whereas the abscissa and ordinate have different signs in II and IV quadrants.

Thus, the points whose abscissa and ordinate have different signs will lie in II and IV quadrants.

Hence, the correct answer is option (d).

Question 20:

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 20:

In I quadrant: x > 0, y > 0

In II quadrant: x < 0, y > 0

In III quadrant: x < 0, y < 0

In IV quadrant: x > 0, y < 0

Thus, the abscissa of the point is positive (x > 0) in I and IV quadrants.

Hence, the correct answer is option (b).

Question 21:

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 formed?
(a) Square
(b) Rectangle
(c) Trapezium
(d) Rhombus

Answer 21:

The given points are O(0, 0), A(3, 0), B(3, 4) and C(0, 4). These points can be plotted on the graph paper as shown below.

From the figure, we have

OA = 3 units, AB = 4 units, BC = 3 units and OC = 4 units

In quadrilateral OABC,

OA = BC = 3 units and AB = OC = 4 cm

Thus, the quadrilateral OABC is a rectangle.

Hence, the correct answer is option (b).

Question 22:

The image of the point (3, 4) in x-axis has the coordinates
(a) (–3, 4)
(b) (3, –4)
(c) (–3, –4)
(d) (4, 3)

Answer 22:

Question 23:

The image of the point (–5, 7) in y-axis has the coordinates
(a) (5, 7)
(b) (–5, –7)
(c) (5, –7)
(d) (7, –5)

Answer 23:

Under reflection of a point in the y-axis, the ordinate of the point remains unchanged while the sign of the abscissa is changed. So, the image of the point (x, y) in the y-axis is (−x, y).

Thus, the image of the point (−5, 7) in the y-axis is (5, 7).

Hence, the correct answer is option (a).

Question 24:

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
(c) y-coordinate = – 5 only
(d) y-coordinate = 5 or –5

Answer 24:

The perpendicular distance of a point from the x-axis gives the ordinate of the point. It is given that the foot of the perpendicular lies on the negative direction of x-axis, so the perpendicular distance can be measured in II or III quadrant.

It is given that, the perpendicular distance of a point P from the x-axis is 5 units and the foot of perpendicular lies on the negative direction of x-axis. So, the point P can be plotted on the graph paper as shown below.

Thus, the point P has y-coordinate as 5 or −5.

Hence, the correct answer is option (d).

Question 25:

If the mirror image of the point P(5, 2) in x-axis is the point Q and the image of Q in y-axis is R. Then the coordinates of R are
(a) (5, –2)
(b) (–5, –2)
(c) (–5, 2)
(d) (2, 5)

Answer 25:

Under reflection of a point in the x-axis, the abscissa of the point remains unchanged while the sign of the ordinate is changed. So, the image of the point (x, y) in the x-axis is (x, −y).

So, the image of the point P(5, 2) in x-axis is Q(5, −2).

Now, under reflection of a point in the y-axis, the ordinate of the point remains unchanged while the sign of the abscissa is changed. So, the image of the point (x, y) in the y-axis is (−x, y).

So, the image of the point Q(5, −2) in y-axis is R(−5, −2).

Thus, the co-ordinates of the point R are (−5, −2).

Hence, the correct answer is option (b).