Question

Three consecutive vertices of a parallelogram $ABCD$ are $A(6,-2,4),B(2,4,-8)$ and $C(-2,2,4)$. Find the coordinates of the fourth vertex.

Answer 1

In parallelogram diagonals bisect each other.

$\frac{x+2}{2}=\frac{6+(-2)}{2}\Rightarrow x+2=4\Rightarrow x=2$

$\frac{y+2}{2}=\frac{-2+2}{0}\Rightarrow y+4=0\Rightarrow y=-4$

$\frac{z+8}{2}=\frac{4+4}{2}\Rightarrow z+8=8\Rightarrow z=0$

$\therefore$ fourth vertex is $(2,-4,0)$