$\Delta ABC$ and its mirror reflection $\Delta A^{\prime}B^{\prime}C^{\prime}$ is arbitrarily placed on the plane. Prove the midpoints of $AA^{\prime},BB^{\prime},CC^{\prime}$ are collinear.
Problem
Source: Tournament of Towns,Spring 2002, Senior O Level, P2
Tags: geometry, geometric transformation, reflection, rotation, geometry proposed