SSC CGL 2025 PYQ — Question 58

The correct answer is Option 1 i.e. (5, 6).

Centroid G = (4, 5), vertex A = (2, 3), D is midpoint of BC.

The centroid divides the median AD in the ratio of 2 : 1. So, AG : GD = 2 : 1

Using section formula for internal division:

If point G divides AD in ratio m : n with A and D as endpoints, then

$G = \left( \frac{m \cdot x_D + n \cdot x_A}{m + n}, \frac{m \cdot y_D + n \cdot y_A}{m + n} \right)$

Here m = AG = 2, n = GD = 1

So, $G_x = \frac{2 \cdot x_D + 1 \cdot x_A}{3}, \quad G_y = \frac{2 \cdot y_D + 1 \cdot y_A}{3}$

Substitute G = (4, 5), A = (2, 3): $4 = \frac{2x_D + 2}{3}$

⇒ $12 = 2x_D + 2$

⇒ $2x_D = 10$

⇒ x_D = 5

$5 = \frac{2y_D + 3}{3}$

⇒ $15 = 2y_D + 3$

⇒ 2y_D = 12

⇒ y_D = 6

So, D = (x_D, y_D) = (5, 6)