Question 17
(ROM) Suppose $ABCD$ and $A^\prime B^\prime C^\prime D^\prime$ are two parallelograms arbitrarily arranged in space, and let points $M,N,P,Q$ divide the segments $AA^\prime,BB^\prime,CC^\prime,DD^\prime$ respectively in equal ratios.
(a) Show that $MNPQ$ is a parallelogram;
(b) Find the locus of $MNPQ$ as $M$ varies along the segment $AA^\prime$.
(a) Show that $MNPQ$ is a parallelogram;
(b) Find the locus of $MNPQ$ as $M$ varies along the segment $AA^\prime$.