Question

Assertion (A): Point $$P(5, -3)$$ is one of the points of trisection of the line segment joining the points $$A(7, -2)$$ and $$B(1, -5)$$.

Reason (R): $$P$$ divides $$AB$$ in the ratio $$2 : 1$$.

Options

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

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

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. The segment from A to B has displacement $$(-6, -3)$$. One-third of this displacement from A is $$(-2, -1)$$, giving $$P(5, -3)$$. Hence, P is a trisection point.

Step 2 – Reason: R is false. Since $$AP = (-2, -1)$$ and $$PB = (-4,-2)$$, their lengths are in the ratio $$AP : PB = 1 : 2$$, not $$2 : 1$$.