Sequencing Reflections and Translations

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Examples, solutions, worksheets, videos, and lessons to help Grade 8 students understand the sequence of reflections and translations.

New York State Common Core Math Grade 8, Module 2, Lesson 8.

Student Outcomes

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
A reflection is always its own inverse.

Exercises

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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