Question

Assertion (A): The points $$A(1, 2), B(-2, 3)$$ and $$C(-3, -4)$$ are not collinear.

Reason (R): $$\operatorname{ar}(\triangle ABC) = 11$$ sq units.

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 area of the triangle formed by the three points is non-zero.

Step 2 – Reason: R is true. Using the coordinate area formula: $$\operatorname{ar}(\triangle ABC) = \frac{1}{2}|7 + 12 + 3| = 11 \text{ sq units}$$

Step 3 – Link: A non-zero area confirms that the points are not collinear; therefore, R correctly explains A.