The co-ordinates of the centroid of a triangle ABC are (-1,-2) what are the co-ordinates of vertex C, if co-ordinates of A and B are (6,-4)  and (-2,2) 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(6,-4) and Vertex B(-2,2) and Centroid = (-1,-2)

=> $$-1 = \frac{-2 + 6 + x}{3}$$

=> $$x + 4 = -1 \times 3 = -3$$

=> $$x = -3 - 4 = -7$$

Similarly, => $$-2 = \frac{-4 + 2 + y}{3}$$

=> $$y - 2 = -2 \times 3 = -6$$

=> $$y = -6 + 2 = -4$$

$$\therefore$$ Coordinates of vertex C = (-7,-4)

=> Ans - (A)