Lesson 7
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004127Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=53c8710f18928b533d8a3d1a26630e9391af10856ec8310cab9ac5e8126b2783)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004127Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=720a5f4af23f3f46841ae5cb3a54b639743430211ed3548db09a8667bc06db2e)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004127Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2fa24feac7ee89f32f62e746ffa4a1d87d031357d29b5e0aea6b2af89f808700)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004127Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=747cd76c5763263b2299f28c1fa8b6e9831d1684747abf9dad29b24014dd90d8)
- Rotate the shape 180 degrees counterclockwise around \(B\).
![Quadrilateral B on a triangular grid.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004127Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3308bd4e00c09aaaf18439c9403f296f759aa9e119c14ee6fbb63e53a4d64524)
- Reflect the shape over the line shown.
![Quadrilateral with one point on line j on a triangular grid.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004127Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e7aee51e34027505124119f31cccc8200ee6c4df0bd0970794ba085355aaa4c9)
Solution
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(From Unit 1, Lesson 4.)