1. 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?
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By: anil on 05 May 2019 01.45 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(7,-1) and Vertex B(1,2) and Centroid = (2,2) => $$2 = frac{7 + 1 + x}{3}$$ => $$x + 8 = 2 imes 3 = 6$$ => $$x = 6 - 8 = -2$$ Similarly, => $$2 = frac{-1 + 2 + y}{3}$$ => $$y + 1 = 2 imes 3 = 6$$ => $$y = 6 - 1 = 5$$ $$ herefore$$ Coordinates of vertex C = (-2,5) => Ans - (A)
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