Co-ordinate Geometry — Assertion-Reason Type Questions

Assertion (A): The coordinates of a point P are (7, 3). The distance of point P from x-axis is 7 units and that from y-axis is 3 units.

Reason (R): x-coordinate of a point is called abscissa and y-coordinate is called ordinate.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true.

4. Both A and R are false.

Answer

As coordinates of P are (7, 3)

So, the distance from x-axis 3 and distance from y-axis is 7.

⇒ Assertion (A) is false .

As x-coordinate of a point is called abscissa and y-coordinate is called ordinate.

⇒ Reason (R) is true.

Hence, option 2 is the correct option.

Assertion (A): The distance between origin (O) and P(4, 3) is given by

OP = $\sqrt{(4)^2 + (3)^2}$ = 5 units

Reason (R): The distance between the points A(x₁, y₁) and B(x₂, y₂) is given by

AB = $\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true.

4. Both A and R are false.

Answer

We will find distance between O and P by using distance formula,

$OP = \sqrt{(4 - 0)^2 + (3 - 0)^2}\\[1em] =\sqrt{4^2 + 3^2}\\[1em] =\sqrt{16 + 9}\\[1em] =\sqrt{25}\\[1em] = 5$

⇒ Assertion (A) is true.

As Distance Formula for two points A and B is

AB = $\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

⇒ Reason (R) is correct.

Hence, option 3 is the correct option.

Assertion (A): The point (0, -2) lies on y-axis.

Reason (R): Any point of the form (0, y) lies on x-axis.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

As, x = 0 and y = -2

Thus, the point (0, -2) lies on y-axis.

⇒ Assertion (A) is true.

Reason (R) states that any point of the form (0, y) lies on the x-axis, which is false. In fact, any point of the form (0, y) lies on the y-axis.

⇒ Reason (R) is false.

Hence, option 1 is the correct option.