Geometry, Please Help!

Question

Here are 2 polygons. Select all sequences of translations, rotations, and reflections below that would take polygon P to polygon Q.

Diagram: https://assets.learnosity.com/organisations/154/0586cb0f-ed0a-4a93-870f-e6ac9596c13f.PNG

A. Reflect over line BA and then translate by directed line segment BA.

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 the line BA and then rotate 60°counterclockwise around point A.

E. Rotate 180° around point A.

Answer 1

You are being asked to describe how to move Polygon P (with the blue outline) to be exactly on top of Polygon Q (with the green outline). For each potential answer, try to follow the steps and see if the Polygon P would end up on top of Polygon Q.

Some examples:

Option E : Rotate 180 degrees around point A.

Imagine putting your finger on point A and spinning Polygon P around your finger. Would it ever land exactly on top of Polygon Q? Since 360 degrees is a full rotation, spinning it 180 degrees is only spinning the shape halfway.

Option C: Translate so that A is taken to J. Then reflect over line BA.

Imagine sliding Polygon P so that point A is now on top of point J. Then, fold your paper on the line connecting points B and A. Would Polygon P land on top of Polygon Q?

If it is hard to visualize all the movements, trace your polygon P onto some paper and then you have a way of physically moving the shape instead of just imagining how it might need to move in order to land on top of Polygon Q.