Explore the relationship between triangle ABC and its reflected image A'B'C' over point P. Drag the vertices and point P to discover the properties of a point reflection.
[list][*]Drag a vertex of [b]ABC[/b]. What changes and what stays the same in [b]A'B'C'[/b]? Drag point [b]P[/b]. How does the image move?[br][/*][/list]
[list][*]What is the relationship between point [b]P[/b] and each pair of corresponding points (e.g., A and A')? (Measure distances or observe midpoints.)[br][/*][/list]
[list][*]How is this "reflection over a point" the same as another type of rigid motion? (Hint: Try mentally rotating ABC 180° around P.)[/*][/list]
[list][*]If point P is at [code](h,k)[/code] and A is at [code](x,y)[/code], what is the coordinate rule for finding A'?[/*][/list]
[list][*]In your own words, define a point reflection. What happens if you reflect a shape twice over the same point P?[/*][/list]