Lesson 6
No Bending or Stretching
Problem 1
Is there a rigid transformation taking Rhombus P to Rhombus Q? Explain how you know.
![Two rhombi, rhombus P and rhombus Q. Rhombus P and Q appear to have the same length bases, but rhombus Q is taller and rhombus P sides have a lower slopes.](https://staging-cms-im.s3.amazonaws.com/1gehNMicYC6otAqLe5ECeXvi?response-content-disposition=inline%3B%20filename%3D%228-8.1.A7.newPP.03.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A7.newPP.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160013Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=047644e2c8d1293561146c6fd91bfb06cb4f4e16da8c835ddbb1b7ee03440466)
Solution
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Problem 2
Describe a rigid transformation that takes Triangle A to Triangle B.
![Triangle A and its image triangle B on a coordinate plane, origin \(O\).](https://staging-cms-im.s3.amazonaws.com/zBBjSqjsHCGVSsaAPB9cvoMG?response-content-disposition=inline%3B%20filename%3D%228-8.1.B.PP.Image.06.6.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.B.PP.Image.06.6.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160013Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5de2234f429a0173f2d5df867e14eeca5dcb7f4bdfca031ef099f9a68918d380)
Solution
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Problem 3
Is there a rigid transformation taking Rectangle A to Rectangle B? Explain how you know.
![Two rectangles, A and B. Rectangle A is tall and thin, and the base is the smaller side. Rectangle B is wider and shorter than rectangle A, and the base is the longer side of B.](https://staging-cms-im.s3.amazonaws.com/gaHfbtD4GR9D7S3FsKLqvSrA?response-content-disposition=inline%3B%20filename%3D%228-8.1.A7.newPP.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A7.newPP.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160013Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=907eba44b76358292f482b4bb9929a88ad8928ffc1149228fa9cd4d0e110aa05)
Solution
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Problem 4
For each shape, draw its image after performing the transformation. If you get stuck, consider using tracing paper.
- Translate the shape so that \(A\) goes to \(A’\).
![Quadrilateral A with point A on the lower left and point A prime on a triangular grid.](https://staging-cms-im.s3.amazonaws.com/QDnwuBAeQtWUME84cW1dNfNy?response-content-disposition=inline%3B%20filename%3D%228-8.1.A.PP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A.PP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160013Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=728ca9eae801db24429a613b8c569ab85d41228bdebc85b80474e19afd72404c)
- Rotate the shape 180 degrees counterclockwise around \(B\).
![Quadrilateral B on a triangular grid.](https://staging-cms-im.s3.amazonaws.com/x3FgviKGF3myMcaBU7eRNdxT?response-content-disposition=inline%3B%20filename%3D%228-8.1.A.PP.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A.PP.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160013Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2d7bd6388970f9d675a250267cb69b120ec821ead9146cff680722f48f056a2c)
- Reflect the shape over the line shown.
![Quadrilateral with one point on line j on a triangular grid.](https://staging-cms-im.s3.amazonaws.com/aR6D26sP998hMVcGHgxQNETC?response-content-disposition=inline%3B%20filename%3D%228-8.1.A.PP.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A.PP.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T160013Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6061a7e917b250f0b19c937cf11a0aa8708f1ef3f86ed5db8fcb5648ac990537)
Solution
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(From Unit 1, Lesson 3.)