Question

Assertion (A): The points $$A(-1, 1), B(5, 7)$$ and $$C(8, 10)$$ cannot be the vertices of a triangle.

Reason (R): $$\operatorname{area}(\triangle ABC) = 0$$.

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 three points are collinear, so they cannot form a triangle. Their area is: $$ \operatorname{area}(\triangle ABC) = \frac{1}{2}|3 + 45 - 48| = 0 $$

Step 2 – Reason: R is true. The area of the triangle formed by these points is zero.

Step 3 – Link: A zero area means the points are collinear and do not form a triangle, so R correctly explains A.