Lesson 7
Rotation Patterns
Problem 1
For the figure shown here,
- Rotate segment \(CD\) \(180^\circ\) around point \(D\).
- Rotate segment \(CD\) \(180^\circ\) around point \(E\).
- Rotate segment \(CD\) \(180^\circ\) around point \(M\).
![Segment C D with midpoint M and C D rising from left to right. Point E is above M D, slightly left of point D.](https://staging-cms-im.s3.amazonaws.com/txRWaAuBCM8MKzUspiwEZPth?response-content-disposition=inline%3B%20filename%3D%228-8.1.B8.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.B8.newPP.01.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=20240722T155415Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b40384765281bb864ec575843edb8f62ecc22818290403ffa4a4d0f31e107e35)
Solution
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Problem 2
Here is an isosceles right triangle:
Draw these three rotations of triangle \(ABC\) together.
- Rotate triangle \(ABC\) 90 degrees clockwise around \(A\).
- Rotate triangle \(ABC\) 180 degrees around \(A\).
- Rotate triangle \(ABC\) 270 degrees clockwise around \(A\).
![Right isosceles triangle A B C has horizonatl side A B with point A to the right of B, and has vertical side B C with point C directly above point B.](https://staging-cms-im.s3.amazonaws.com/Dk2Lso72x9fZ6MnDTYZpzGQZ?response-content-disposition=inline%3B%20filename%3D%228-8.1.Cycle4.4.5.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.Cycle4.4.5.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=20240722T155415Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=bb4f3e83c0b40e8b63b8bf1bf12dbab0d9da319caa1e752d038faa1305c97f94)
Solution
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Problem 3
Each graph shows two polygons \(ABCD\) and \(A’B’C’D’\). In each case, describe a sequence of transformations that takes \(ABCD\) to \(A’B’C’D’\).
Solution
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(From Unit 1, Lesson 4.)Problem 4
Lin says that she can map Polygon A to Polygon B using only reflections. Do you agree with Lin? Explain your reasoning.
![Two quadrilaterals polygon A and B on a grid.](https://staging-cms-im.s3.amazonaws.com/YQm8XWwhyWjMScV2a8anpNc3?response-content-disposition=inline%3B%20filename%3D%228-8.1.A.PP.Image.21.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.A.PP.Image.21.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=20240722T155415Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=deafb98035aa3040b96f14093993fad7ce064020901186c063990f6d9efabebe)
Solution
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(From Unit 1, Lesson 3.)