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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T025041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c517c104a24f081cc9c8cadcf8fcd680ea0948dbf49c8d67f680fa1e7fa3588e)
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=20240727T025041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ca9af22572c5f7d2e41ecc7bd03de087c1836b75a877e22499f079596c2a3d68)
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=20240727T025041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=792f54faccac9ba93cb276c62ff6e9db57d91527943653266fde905397645dfa)
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=20240727T025041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=998d50497c18ce22bf1ac66bae93b9bd4309c313ae9cefebb9d7c3e09b3175e8)
- 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=20240727T025041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a6fb83d54d49898b90e8a9ef42a9e71175676fb2f4496a225d27c40a3a90b2d9)
- 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=20240727T025041Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8ea47ee97b30a172c07225d625db4411e507682b413fc58a14c7fb13cb6139b0)