A (3, 2) and B (-2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates (5/3, - 1/3). Find the coordinates of the third vertex C of the triangle.

Question

Philoid · Accepted Answer

Let the vertex of the triangle be A(3, 2), B(-2, 1) and C(x, y)

Let the centroid be G(, ), as it is given that centroid is given at origin.

We know that centroid of a triangle for (x₁ , y₁), (x₂ , y₂) and (x₃ , y₃) is

G(x, y) = ( , )

For given coordinates A(3, 2), B(-2, 1) and C(x, y)

(, ) = , )

Solving for x and y,

-3 + 2 +x =5 and 2 + = -1

∴ x = 4 and y = -4

Hence, the coordinate of third vertex is C(4, -4).