Question 6
(ROM) A plane $\epsilon$ is given and on one side of the plane three noncollinear points $A,B$, and $C$ such that the plane determined by them is not parallel to $\epsilon$. Three arbitrary points $A',B'$, and $C'$ in $\epsilon$ are selected. Let $L,M$, and $N$ be the midpoints of $AA',BB'$, and $CC'$, and $G$ the centroid of $\triangle LMN$. Find the locus of all points obtained for $G$ as $A',B'$, and $C'$ are varied (independently of each other) across $\epsilon$.