Question

Show that the points $A(1,2,3)$, $B(-1,-2,-3)$, $C(2,3,2)$ and $D(4,7,3)$ are the vertices of a parallelogram.

Answer 1

If the given points are vertices of a parallelogram then coordinates of mid point of $AC$ and $BD$ should be equal.

$(\frac{1+2}{2},\frac{2+3}{2},\frac{3-3}{2})=(\frac{-1+4}{2},\frac{-2+7}{2},\frac{-3+3}{2})$

$(\frac{3}{2},\frac{5}{2},0)=(\frac{3}{2},\frac{5}{2},0)$

Hence, proved.