If two vertices of a triangle are (5, 4) and (-2, 4) and centroid is (5, 6), then third vertex is:

(12, 10)

The correct answer is Option (2) → (12, 10)

Let the vertices of the triangle be $A(5,4), B(-2,4), C(x, y)$.

The centroid formula:

$G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$

Given $G = (5, 6)$:

$\frac{5 + (-2) + x}{3} = 5 ⇒ \frac{3 + x}{3} = 5 ⇒x + 3 = 15 ⇒x = 12$

$\frac{4 + 4 + y}{3} = 6 ⇒\frac{8 + y}{3} = 6 ⇒8 + y = 18 ⇒y = 10$

Third vertex: $C = (12, 10)$