The co-ordinates of the centroid of a triangle ABC are (2 , 2). What are the co-ordinates of vertex C if co-ordinates of A and B are (7 , -1) and (1 , 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(7,-1) and Vertex B(1,2) and Centroid = (2,2)

=> $$2 = \frac{7 + 1 + x}{3}$$

=> $$x + 8 = 2 \times 3 = 6$$

=> $$x = 6 - 8 = -2$$

Similarly, => $$2 = \frac{-1 + 2 + y}{3}$$

=> $$y + 1 = 2 \times 3 = 6$$

=> $$y = 6 - 1 = 5$$

$$\therefore$$ Coordinates of vertex C = (-2,5)

=> Ans - (A)