Question

Assertion (A): The points $$A(2, -2), B(-3, 8)$$ and $$C(-1, 4)$$ are collinear.

Reason (R): $$BC + AC = AB$$.

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

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

Explanation:

Step 1 – Assertion: A is true. The distances are $$AB = 5\sqrt{5}$$, $$BC = 2\sqrt{5}$$ and $$AC = 3\sqrt{5}$$, so the points are collinear.

Step 2 – Reason: R is true, since $$BC + AC = 2\sqrt{5} + 3\sqrt{5} = 5\sqrt{5} = AB$$.

Step 3 – Link: The sum of the two smaller distances equals the largest distance, so the points lie on one straight line, with C between A and B. Hence R explains A.