Students learn that the reflection is its own inverse transformation.
Students understand that a sequence of a reflection followed by a translation is not equal to a translation followed by a reflection.Classwork
Use the figure below to answer Exercises 1–3.
1. Figure A was translated along vector BA resulting in Translation (Figure A). Describe a sequence of translations that would map Figure A back onto its original position.
2. Figure A was reflected across line resulting in Reflection (Figure A). Describe a sequence of reflections that would map Figure A back onto its original position.
3. Can Translation BA undo the transformation of Translation DC? Why or why not?
4. Let there be the translation along vector AB and a reflection across line L. Use a transparency to perform the following sequence: Translate figure S, then reflect figure S. Label the image S'.
5. Let there be the translation along vector AB and a reflection across line L. Use a transparency to perform the following sequence: Reflect figure S, then translate figure S. Label the image S''.
7. Does the same relationship you noticed in Exercise 6 hold true when you replace one of the translations with a reflection. That is, is the following statement true: A translation followed by a reflection is equal to a reflection followed by a translation?Summary
We know that we can sequence rigid motions.
We have notation related to sequences of rigid motions.
We know that a reflection is its own inverse.
We know that the order in which we sequence rigid motions matters.
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