Lesson 6
No Bending or Stretching
Let’s compare measurements before and after translations, rotations, and reflections.
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034105Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7184cf8b5a10a4919fca97f04dc9b7d7aae14ad1f27284a9b9095fcedb9a0044)
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034105Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f4181406a1d0d9b60244836106b4c5bacf7c82766f724d855b26b9fa63799018)
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034105Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6fa282a9120814f494ad24e6b1a970eaaf1902d4f724384021fa96f406393736)
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034105Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ee3b5de35d705fcd01995912d548c04734ab2224d83f7cc5b63ed8d561a6edbb)
- 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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034105Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=674934207596cc1a58c661b11d428fdf6ed109bab68e445cb59779082e129925)
- 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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034106Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6453fb78da31b4b4f9c388778f1f29f8076657c1816a53e2770d79435132774a)