#### Chapter 11 Co-ordinate Geometry R.D. Sharma Solutions for Class 9th MCQ's

**Multiple Choice Questions**

Q1. 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

**Solution**

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 (0, 0).

Example is shown in the graph

2. The abscissa and ordinate of the origin are

(a) (0, 0)

(b) (1, 0)

(c) (0, 1)

(d) (1, 1)

**Solution**

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 (0, 0).

Thus the correct answer is (a).

3. The measure of the angle between the coordinate axes is

(a) 0°

(b) 90°

(c) 180°

(d) 360°

**Solution**

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 90°.

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

**Solution**

As shown in graph that a point whose abscissa and ordinate are 2 and -5 respectively lies in the fourth quadrant.

5. Points (-4, 0) and (7, 0) lie

(a) on x-axis

(b) y-axis

(c) in first quadrant

(d) In second quadrant

**Solution**

Let the points P and Q whose coordinates are (-4,0) and (7, 0) respectively. Locate the points and you will see that they lie on x-axis.

6. The ordinate of any point on x-axis is

(a) 0

(b) 1

(c) −1

(d) any number

**Solution**

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 (x, 0)

Thus the correct answer is (a).

7. The abscissa of any point on y-axis is

(a) 0

(b) 1

(c) −1

(d) any number

**Solution**

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 (0, y).

Thus the correct answer is (a).

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

**Solution**

The signs of coordinates (x, y) of a point in various quadrants are shown in the following graph:

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

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

**Solution**

As we know that

In the first quadrant : x >0, y>0

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

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

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

Thus the correct answer is (b).

10. Two points having same abscissas 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

**Solution**

Let the points P(3, 5) and Q(3, 2) having the same abscissa but different ordinates be shown in the graph given below:

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

Thus the correct answer is (c).

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

(a) 4

(b) 3

(c) 5

(d) none of these

**Solution**

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

(a) 4

(b) 3

(c) 5

(d) none of these

**Solution**

The point P (4, 3) is shown in the graph given below:

Thus the correct answer is (a).

13. The distance of the point P (4, 3) from the origin is

(a) 4

(b) 3

(c) 5

(d) 7

**Solution**

The point P(4, 3) is shown in the graph given below:

14. The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is

(a) 24 sq. units

(b) 12 sq. units

(c) 10 sq. units

(d) none of these

**Solution**

Given that points A(2, 0) , B(6, 0) and C(4, 6) , form a triangle which is shown in the figure. We are asked to find the area of the triangle ΔABC.

15. The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is

(a) 16 sq. units

(b) 8 sq. units

(c) 4 sq. units

(d) 6 sq. units

**Solution**

Given that the points P(0, 1) , Q(0, 5) and R(3, 4) form a triangle.

We are asked to find the area of the triangle ΔPQR which is shown in the figure.