Question

Assertion (A): The centroid of $$\triangle ABC$$ having vertices $$A(-1, 0), B(5, -2)$$ and $$C(8, 2)$$ is $$G(4, 0)$$.

Reason (R): The centroid of $$\triangle ABC$$ having vertices $$A(x_{1}, y_{1}), B(x_{2}, y_{2})$$ and $$C(x_{3}, y_{3})$$ is given by $$G = \left(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}\right).$$

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. Applying the centroid formula gives: $$G = \left(\frac{-1 + 5 + 8}{3}, \frac{0 + (-2) + 2}{3}\right) = (4,0)$$

Step 2 – Reason: R is true. It states the formula for the centroid of a triangle.

Step 3 – Link: Substituting the three vertices into the stated formula gives $$G(4, 0)$$, so R correctly explains A.