Lesson 7
Rotation Patterns
Let’s rotate figures in a plane.
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T041121Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=116a6a55b440a8152ee68eb17980145e46e8dbdedb418ac69151e71bd8b2dd21)
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T041121Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=07d366d3c9d9cd9bfa32212ecef47993cc8f8c54e0bee094400f22c861de7a38)
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 \(A’B’C’D’\).
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T041121Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2780035a668cd14b7e7a68c55e3023e50f2e1d9b07fcc254c1b41fd255492bf8)