In a ΔPQR, the centroid is at G(1, 2). If the vertices P…

In a ΔPQR, the centroid is at G(1, 2). If the vertices P and Q are at (3, -1) and (-2, 4) respectively, what are the coordinates of vertex R?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. (2, 3).

Let the coordinate of vertex R = (x_R, y_R)

Centroid formula: $G = \left( \frac{x_P + x_Q + x_R}{3}, \frac{y_P + y_Q + y_R}{3} \right)$

So, $1 = \frac{3 + (-2) + x_R}{3}$

⇒ $1 = \frac{1 + x_R}{3}$

⇒ 3 = 1 + x_R

⇒ x_R = 2

$2 = \frac{-1 + 4 + y_R}{3}$

⇒ $2 = \frac{3 + y_R}{3}$

⇒ 6 = 3 + y_R

⇒ y_R = 3

Coordinate of vertex R = (2, 3)

SSC CGL 2025 PYQ — Question 58