Question

Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1

Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Assertion (A) is true, but Reason (R) is false.

Explanation:

The coordinates of the point that divides a line segment with endpoints (x₁, y_1​) and (x₂, y₂​) in the ratio m:n are given by the section formula:

`((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))`

Here, if the point (−3, k) divides the segment in the ratio 1: 2 between (−5, 4) and (−2, 3), then we can plug these values into the section formula:

`- 3 = (1(-2) + 2(-5))/(1 + 2)`

`- 3 = (- 2 - 10)/3`

`-3 = -4`

This is not true. Therefore, the x - x-coordinate does not satisfy the 1:2 division ratio.