Question

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of

A and B are (3, -5, 7) and (-1, 7, -6) respectively, find the coordinates of

the point C.

Answer 1

Let G be the centroid of $△ABC$

Given : G $\equiv$ (1, 1, 1)

Let C $\equiv$ (x, y, z)

Then, 1 = $\frac{3-1+x}{3}$

$\Rightarrow 3=3-1+x$

$\Rightarrow 3=2+x\Rightarrow x=1$

and 1 = $\frac{-5+7+y}{3}$

$\Rightarrow 3=2+y$

$\Rightarrow y=1$

and 1 = $\frac{7-6+z}{3}$

$\Rightarrow 3=1+z$

$\Rightarrow$ z = 2