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%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123559Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=22733c7ceabed82d9d46638edda526add14fc2e2eadae6064d8b96b79748a92f)
Solution
For access, consult one of our IM Certified Partners.
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%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123559Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fbdb44966afa39144e41e8f021be58267dff5e50e7c660cccb145abbbdbb2a4c)
Solution
For access, consult one of our IM Certified Partners.
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%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123559Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0ed8c4728a101bb4f821fa2f276e35778b3b8b4e6b9097d2f23702572de325b9)
Solution
For access, consult one of our IM Certified Partners.
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%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123559Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0b430bc743b3f84196f867a316b4dc6715f1566adc24987114371388976984bc)
- 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%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123559Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=aaae1a524aefbfd30fc4b6fc55e6b8e7a6f55ade368288b3c4cde458db8ec4bd)
- 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%2F20250121%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20250121T123559Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=29c00aebb4bf9701e96f4aa102ac548155aeb2720ff57a4c37d9d035ac7f3855)
Solution
For access, consult one of our IM Certified Partners.
(From Unit 1, Lesson 4.)