If two vertices of a triangle are (5, 4) and (-2, 4) and centroid is (5, 6), then third vertex is:
Answer & explanation
Correct answer: option 2
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: $C = (12, 10)$