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://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=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T032433Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=23ef4b3810fbb9939c2af6a4be969997b48297cb4a63ad6eb5b677780d779e5b)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T032433Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0235a893bb19e246afd9e6380271bc50afd4a17268c5c3ec26ccb0cde9d4e8cb)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T032433Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f1c6f647a6556f21b3b457d94e5f6aaab1ee223a5b145ebf2428db0492bd52a5)