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

Worksheets for Grade 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?

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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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