Note that this open investigation can be taken to many levels of complexity.
Draw a quadrilateral and label its vertices $A, B, C$ and $D$. Pick any point $P_0$ outside the quadrilateral. Apply the following operations to generate eight new points:
Explore the properties of this sequence and its continuation. You might like to use geogebra or other tools alongside a pen and paper analysis.
For more investigations see our Stage 5 pages.