Composition of 3 reflections - General position
- Tibor Marcinek
What is the result of the composition of these 3 reflections Ra' Rb' Rc' ? Step 1:
- Reflect the given shape in the order given above.
- Format the intermediary images and the final image (color, transparency) to make the resulting isometry visually clean.
- Observe the preimage (original brown shape) and the final image. Can you see what the resulting isometry is?
- Use the red slider to rotate b' and c' until b' is perpendicular to a' .
- Use the blue slider to rotate a' and b' until a' || c'.
Can you use this applet to explain why we don't have a "turn reflection" in our list? Hint: The original line arrangement can be though of as a turn reflection: Ra' Rb' generate a rotation (What's its center and angle? Make sure you see it in your intermediary images). Adding Rc' makes it a "turn reflection". Now show that by rotating the lines as we did in step 2 will replace the first rotation Ra' Rb' by a different isometry.