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Reflection in a Square

Point E is reflected in the sides of the square. Drag E to see the change in the images. What properties do you notice in the quadrilateral formed by the red points? By dragging E to different positions, what kind of quadrilaterals can be made.
If we start with other shapes (instead of a square) for generating the mirror images, what different results will we have? In what other ways would you extend this problem?