Question

Assertion (A): The coordinates of the centroid of a triangle whose vertices are (–1, –4), (4, 3) and (6 – 2) are (3, –1).

Reason (R): If the vertices of a triangle are \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right)\) and \(\left(x_{3}, y_{3}\right)\), then the coordinates of its centroid are \(\left(\frac{x_{1} + x_{2} + x_{3}}{2}, \frac{x_{1} + x_{2} + x_{3}}{2}\right)\)

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is true, but R is false.

Explanation:

Centroid is $$G = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) = \left(\frac{-1 + 4 + 6}{3}, \frac{-4 + 3 - 2}{3}\right) = (3, -1).$$ So A is true. R is false because it uses denominator 2 instead of 3.