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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T142246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b4f8399634720bb0f5223d245487493106a5da29e5542202c4388ca89a78af45)
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=20240722T142246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=19a3ada4682e83bf716e058671baa6437cf0d62a9ba9eaaf8ebe836c2ccd8138)
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T142246Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=337bb66e9bed51ec317146850fa47ef2fe9b77d980da7cd0b63ff8bed4a8fbcb)