1. 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?
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By: anil on 05 May 2019 02.10 am
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) => $$-1 = frac{-2 + 6 + x}{3}$$ => $$x + 4 = -1 imes 3 = -3$$ => $$x = -3 - 4 = -7$$ Similarly, => $$-2 = frac{-4 + 2 + y}{3}$$ => $$y - 2 = -2 imes 3 = -6$$ => $$y = -6 + 2 = -4$$ $$ herefore$$ Coordinates of vertex C = (-7,-4) => Ans - (A)
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