1. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Grab a new assignment sheet for October on the front table and gather up your warm ups for September
If you need to staple them together, do so now.
Make sure your name is on them.
Have them ready to turn in after your assignment sheet has been stamped
Tie To LO

2. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Activating Prior Knowledge-
In the diagram, circle R has been translated along vector 𝐴𝐵 . A R B
1. What label should be given to the image of R? 𝑅′
2. What vector will move the image of R back to the location of R? 𝐵𝐴
Tie To LO

3. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Lesson Objective:
Today, we will learn that the reflection is its own inverse transformation and understand that a sequence of a reflection followed by a translation is not equal to a translation followed by a reflection.

4. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Concept Development
Use the figure below to answer Exercises 1–3.
CFU

5. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Concept Development
Exercise 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.
Translate Figure A along vector 𝐵𝐴 ; then, translate the image of Figure A along vector 𝐴𝐵 .
CFU

6. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Concept Development
Exercise 2: Figure A was reflected across line 𝐿 resulting in 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛(𝐹𝑖𝑔𝑢𝑟𝑒 𝐴). Describe a sequence of reflections that would map Figure A back onto its original position.
Reflect Figure A across line 𝐿; then, reflect 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 (𝐹𝑖𝑔𝑢𝑟𝑒 𝐴) back across line 𝐿.
CFU

7. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Concept Development
Exercise 3: Can 𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 𝐵𝐴 of Figure A undo the transformation of 𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝐶 of Figure A? Why or why not?
No. Because 𝐵𝐴 is not going in the exact opposite direction as 𝐷𝐶 , the 𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 𝐵𝐴 will not undo the transformation of 𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝐶
CFU

8. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Concept Development
Exercise 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′.
Let 𝑆 be the black figure.
CFU

9. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Concept Development
Exercise 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′′.
Let 𝑆 be the black figure.
Does the order in which you perform transformations matter?
CFU

10. Complete Exercises 6 – 7 in your modules.
Module 2 LSN 8
Sequencing Reflections and Translations
Independent Practice
Complete Exercises 6 – 7 in your modules.
CFU

11. Sequencing Reflections and Translations
Module 2 LSN 8
Sequencing Reflections and Translations
Closure
1. What did you learn?
2. Why is it important?
3. Does the sequence of a translation and reflection equal the sequence of a reflection and translation? Explain.
Homework: Problem Set 1 – 3 Pg. S. 44
CFU