The co-ordinates of the centroid of a triangle ABC are (3,2). What are the co-ordinates of vertex C if co-ordinates of A and B are (-2,5) and (6,2) respectively?

Coordinates of centroid of triangle with vertices $$(x_1 , y_1)$$ , $$(x_2 , y_2)$$ and $$(x_3 , y_3)$$ is $$(\frac{x_1 + x_2 + x_3}{3} , \frac{y_1 + y_2 + y_3}{3})$$

Let coordinates of vertex C = $$(x , y)$$

Vertex A(-2,5) and Vertex B(6,2) and Centroid = (3,2)

=> $$3 = \frac{-2 + 6 + x}{3}$$

=> $$x + 4 = 3 \times 3 = 9$$

=> $$x = 9 - 4 = 5$$

Similarly, => $$2 = \frac{5 + 2 + y}{3}$$

=> $$y + 7 = 2 \times 3 = 6$$

=> $$y = 6 - 7 = -1$$

$$\therefore$$ Coordinates of vertex C = (5,-1)

=> Ans - (B)