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Reflection about a point

Autor:Allan Canonigo

Your Task

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.

  • Drag a vertex of ABC. What changes and what stays the same in A'B'C'? Drag point P. How does the image move?

  • What is the relationship between point P and each pair of corresponding points (e.g., A and A')? (Measure distances or observe midpoints.)

  • How is this "reflection over a point" the same as another type of rigid motion? (Hint: Try mentally rotating ABC 180° around P.)

  • If point P is at (h,k) and A is at (x,y), what is the coordinate rule for finding A'?

  • In your own words, define a point reflection. What happens if you reflect a shape twice over the same point P?

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