Question

select all sequences of translations, rotations, and reflections below that would take polygon p to polygon q.
rotate 180 degrees around point a.
rotate 60 degrees counter - clockwise around point a and then reflect over the line fa.
translate so that a is taken to j. then reflect over line ba.
reflect over line ba, then translate by directed line segment ba.
reflect over line ba and then rotate 60 degrees counter - clockwise around point a.

Explanation:

1. Analyze each transformation option:

• For rotation of 180 - degrees around point A, it may not align polygon P to polygon Q.
• Rotating 60 - degrees counter - clockwise around point A and then reflecting over line FA can map polygon P to Q as the rotation changes the orientation and the reflection aligns it properly.
• Translating A to J and then reflecting over line BA may not work as the initial translation may mis - align the polygons before reflection.
• Reflecting over line BA and then translating by directed line segment BA can also map polygon P to Q as the reflection flips the polygon and the translation moves it to the correct position.
• Reflecting over line BA and then rotating 60 - degrees counter - clockwise around point A may not result in the correct mapping as the order of operations can mis - align the polygons.

Answer:

B. Rotate 60 degrees counterclockwise around point A and then reflect over the line FA.
D. Reflect over line BA, then translate by directed line segment BA.