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? ?->(Show Answer!)

1. 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?

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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(-2,5) and Vertex B(6,2) and Centroid = (3,2) => $$3 = frac{-2 + 6 + x}{3}$$ => $$x + 4 = 3 imes 3 = 9$$ => $$x = 9 - 4 = 5$$ Similarly, => $$2 = frac{5 + 2 + y}{3}$$ => $$y + 7 = 2 imes 3 = 6$$ => $$y = 6 - 7 = -1$$ $$ herefore$$ Coordinates of vertex C = (5,-1) => Ans - (B)

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