Problem

Source: Central American Olympiad 2000, problem 3

Tags: geometry, parallelogram, trigonometry, analytic geometry, graphing lines, slope, complex numbers



Let $ ABCDE$ be a convex pentagon. If $ P$, $ Q$, $ R$ and $ S$ are the respective centroids of the triangles $ ABE$, $ BCE$, $ CDE$ and $ DAE$, show that $ PQRS$ is a parallelogram and its area is $ 2/9$ of that of $ ABCD$.