If the centroid of a triangle is at (1, 3) and two of its vertices are (–7, 6) and (8, 5) then find the third vertex of the triangle.

Question

Philoid · Accepted Answer

Let A (–7, 8), B (8, 5) and C (a, b) are three vertices of the triangle and centroid of the triangle is (1, 3)

The centroid G (x_, y) of a triangle whose vertices are (x_1, y₁), (x_2, y₂) and (x₃, y₃) is given by:

G (x, y) =

⇒ (1, 3) =

and

1 + a = 3× 1 and 11 + b = 3 × 3

1 + a = 3 and 11 + b = 9

a = 3 – 1 and b = 9 – 11

a = 2 and b = –2

Therefore, the missing vertex of the triangle is (2, –2).