Question

here are 2 polygons: practice 5 (from unit 1, lesson 13) select all sequences of translations, rotations, and reflections below that would take polygon p to polygon q. a rotate 180° around point a. b translate so that a is taken to j. then reflect over line ba. c rotate60° counterclockwise around point a and then reflect over the line fa. d reflect over the line ba and then rotate 60° counterclockwise around point a. e reflect over line ba and then translate by directed line segment ba.

Explanation:

Step1: Analyze transformation A

A 180 - degree rotation around point A changes the orientation of polygon P. Then, no further operations are mentioned in a way that would clearly map it to polygon Q. So, A is not correct.

Step2: Analyze transformation B

Translating so that A is taken to J changes the position. Reflecting over line BA after that may not map polygon P to Q as the initial translation and subsequent reflection combination is not likely to match the required transformation. So, B is not correct.

Step3: Analyze transformation C

Rotating 60 - degrees counter - clockwise around point A changes the orientation. Reflecting over line FA after that may not map polygon P to Q as the combination of rotation and reflection does not seem to align the polygons. So, C is not correct.

Step4: Analyze transformation D

Reflecting over line BA changes the orientation with respect to that line. Then rotating 60 - degrees counter - clockwise around point A can further adjust the position and orientation. This combination can map polygon P to Q.

Step5: Analyze transformation E

Reflecting over line BA changes the orientation. Translating by directed line segment BA changes the position. This combination can map polygon P to Q.

Answer:

D. Reflect over the line BA and then rotate 60° counterclockwise around point A;
E. Reflect over line BA and then translate by directed line segment BA