Co-ordinate Geometry — Multiple Choice Questions

Which point lies on x-axis?

1. (3, 2)

2. (-3, 2)

3. (2, 0)

4. (-1, -2)

Answer

As y = 0 on x-axis, the point (2, 0) lies on x-axis.

Hence, option 3 is the correct option.

Which point lies on y-axis?

1. (1, 3)

2. (0, 3)

3. (5, 2)

4. (-2, -3)

Answer

As x = 0 on y-axis, the point (0, 3) lies on y-axis.

Hence, option 2 is the correct option.

Which point lies in IV quadrant?

1. (-2, -3)

2. (1, -4)

3. (-2, 3)

4. (0, 1)

Answer

In the IV quadrant, x is positive and y is negative.

So, the point (1, -4) lies in the IV quadrant.

Hence, option 2 is the correct option.

Which point lies in III quadrant?

1. (0, 3)

2. (2, 0)

3. (7, 2)

4. (-2, -3)

Answer

In the III quadrant, both x and y are negative.

So, the point (-2, -3) lies in the III quadrant.

Hence, option 4 is the correct option.

Which graph is parallel to x-axis?

1. y = x + 1

2. y = 2

3. x = 3

4. x = 2y

Answer

A line parallel to the x-axis has the form y = constant.

So, y = 2 is parallel to x-axis.

Hence, option 2 is the correct option.

P is a point on x-axis at a distance of 3 units from y-axis to its right. The coordinates of P are :

1. (3, 0)

2. (0, 3)

3. (3, 3)

4. (-3, 3)

Answer

P is on x-axis, then its y coordinate is 0.

Distance is 3 units from y-axis to its right.

Thus, x-coordinate is positive.

⇒ x = 3

So, coordinates of P = (3, 0).

Hence, option 1 is the correct option.

The distance of the point P(4, -3) from the origin is :

1. 1 unit

2. 7 units

3. 5 units

4. 3 units

Answer

Let O(0, 0) be the origin.

Using distance formula,

PO = $\sqrt{(0 - 4)^2 + (0 - (-3))^2}$

= $\sqrt{(-4)^2 + (3)^2}$

= $\sqrt{16 + 9} = \sqrt{25}$

= 5 units.

Hence, option 3 is the correct option.

What point on x-axis is equidistant from the points A(7, 6) and B(-3, 4)?

1. (0, 4)

2. (-4, 0)

3. (3, 0)

4. (0, 3)

Answer

Let the point on x-axis be P(x, 0) which is equidistant from the points A(7, 6) and B(-3, 4).

As point is equidistant from the points A and B.

Distance of A and P = Distance of P and B

AP = PB

$\Rightarrow \sqrt{(x - 7)^2 + (0 - 6)^2} = \sqrt{(- 3 - x)^2 + (4 - 0)^2}$

Squaring both sides, we get :

⇒ (x - 7)² + (-6)² = (-3 - x)² + 4²

⇒ x² + 49 - 14x + 36 = x² + 9 + 6x + 16

⇒ -14x + 85 = 6x + 25

⇒ -14x - 6x - 25 + 85 = 0

⇒ -20x + 60 = 0

⇒ 20x = 60

⇒ x = 3

∴ P(3, 0) is the point on x-axis which is equidistant from the points A(7, 6) and B(-3, 4).

Hence, option 3 is the correct option.