Sequencing Translations

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

New York State Common Core Math Grade 8, Module 2, Lesson 7

Worksheets and solutions for Common Core Grade 8, Module 2, Lesson 7

Student Outcomes

Students learn about the sequence of transformations (one move on the plane followed by another) and that a sequence of translations enjoy the same properties as a single translation with respect to lengths of segments and degrees of angles.

Students learn that a translation along a vector followed by another translation along the same vector in the opposite direction can move all points of a plane back to its original position.

Exploratory Challenge

1. a. Translate ∠ ABC and segment ED along vector FG. Label the translated images appropriately, i.e. A'B'C' and E'D'.

b. Translate ∠ A'B'C' and segment E'D' along vector FG. Label the translated images appropriately, i.e. A''B''C'' and E''D''.

c. How does the size of ∠ ABC compare with the size of ∠ A''B''C'' ?

d. How does the length of segment ED compare to the length of the segment E''D''?

e. Why do you think what you observed in parts (d) and (e) were true?

2. Translate triangle ABC along vector FG and then translate its image along vector JK. Be sure to label the images appropriately.

3. Translate figure ABCDEF along vector GH. Then translate its image along vector JL appropriately.

4. a. Translate Circle A and Ellipse E along vector AB . Label the images appropriately.

a. Translate Circle A' and Ellipse E' along vector CD . Label the images appropriately.

c. Did the size or shape of either figure change after performing the sequence of translations? Explain.

If a figure undergoes to two transformations and ends up in the same place as it was originally, we say that the figure has been mapped to itself.

5. The picture below shows the translation of Circle A along vector CD . Name the vector that will map the image of Circle A back onto itself.

6. If a figure is translated along vector QR , what translation takes the figure back to its original location?

Lesson Summary

Translating a figure along one vector then translating its image along another vector is an example of a sequence of transformations.

A sequence of translations enjoys the same properties as a single translation. Specifically, the figures’ lengths and degrees of angles are preserved.

If a figure undergoes two transformations, F and G, and is in the same place it was originally, then the figure has been mapped onto itself.

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