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A(-4, 4), B(x, -1) and C(6, y) are the vertices of △ABC. If the centroid of this triangle ABC is at the origin, find the values of x and y.

Section Formula

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Answer

By formula,

Centroid of triangle = (x1+x2+x33,y1+y2+y33)\Big(\dfrac{x1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3}\Big)

Given,

Centroid of triangle = (0, 0)

Substituting values for x-coordinate we get,

⇒0=(−4+x+63)⇒−4+x+6=0⇒x+2=0⇒x=−2.\Rightarrow 0 = \Big(\dfrac{-4 + x + 6}{3}\Big) \\[1em] \Rightarrow -4 + x + 6 = 0 \\[1em] \Rightarrow x + 2 = 0 \\[1em] \Rightarrow x = -2.

Substituting values for y-coordinate we get,

⇒0=(4+(−1)+y3)⇒4−1+y=0⇒y+3=0⇒y=−3.\Rightarrow 0 = \Big(\dfrac{4 + (-1) + y}{3}\Big) \\[1em] \Rightarrow 4 - 1 + y = 0 \\[1em] \Rightarrow y + 3 = 0 \\[1em] \Rightarrow y = -3.

Hence, x = -2 and y = -3.

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