Question

select all sequences of translations, rotations, and reflections below that would take polygon p to polygon q.
a. rotate 180° around point a.
b. rotate 60° counterclockwise around point a and then reflect over the line fa.
c. translate so that a is taken to j. then reflect over line ba.
d. reflect over line ba and then translate by directed line segment ba.
e. reflect over the line ba and then rotate 60° counterclockwise around point a.

Explanation:

Step1: Analyze transformation a

A 180 - degree rotation around point A changes the orientation of polygon P. Then reflecting over line FA can map it to polygon Q.

Step2: Analyze transformation b

A 60 - degree counter - clockwise rotation around point A changes the orientation. Reflecting over line BA after that may not necessarily map P to Q as the 60 - degree rotation might not align the polygon correctly for the reflection to result in Q.

Step3: Analyze transformation c

Translating point A to J changes the position of the polygon. Then reflecting over line BA may not map P to Q as the initial translation and subsequent reflection combination may not be correct.

Step4: Analyze transformation d

Reflecting over line BA and then rotating 60 - degree counter - clockwise around point A may not map P to Q as the order and nature of these transformations may not align the polygons.

Step5: Analyze transformation e

Reflecting over line BA and then rotating 60 - degree counter - clockwise around point A may not map P to Q for the same reasons as in d.

Answer:

a. Rotate 180° around point A. Then reflect over the line FA.