Let the vertex of the triangle be A(3, 2), B(-2, 1) and C(x, y)
Let the centroid be G(\(\frac{5}3\) , \(\frac{-1}3\)), 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) = \(
(\frac{x_1+x_2+x_3}3,\frac{y_1+y_2+y_3}3)\)
For given coordinates A(3, 2), B(-2, 1) and C(x, y)
G(\(\frac{5}3\) , \(\frac{-1}3\)) = \(
(\frac{3-2+x}3,\frac{2+1+y}3)\)
Solving for x and y,
-3 + 2 +x =5 and 2 + 1 + y = -1
∴ x = 6 and y = -4
Hence,
the coordinate of third vertex is C(6, -4).