Question

select all the ways we could describe the rigid transformation that takes aefs to cfed. a. reflect aefs across line ef. b. rotate aefs 180 degrees counterclockwise around point g. c. rotate aefs 180 degrees clockwise around point g. d. translate aefs by the directed line segment from f to e. then reflect across line fe. e. translate aefs by the directed line segment from f to e. then rotate 180° clockwise around point e.

Explanation:

Step1: Analyze rigid - transformation properties

Rigid transformations include reflections, rotations, and translations and preserve shape and size.

Step2: Check option A

Reflecting $\triangle AEF$ across line $EF$ will not map it to $\triangle CFE$ as the orientation and position will be wrong.

Step3: Check option B

Rotating $\triangle AEF$ 180 degrees counter - clockwise around point $G$ will map $\triangle AEF$ to $\triangle CFE$ since point $G$ is the mid - point of $AC$ and $EF$, and 180 - degree rotation is a central symmetry transformation.

Step4: Check option C

Rotating $\triangle AEF$ 180 degrees clockwise around point $G$ will also map $\triangle AEF$ to $\triangle CFE$ for the same reason as in option B.

Step5: Check option D

Translating $\triangle AEF$ by the directed line segment from $F$ to $E$ and then reflecting across line $FE$ will not map it to $\triangle CFE$ as the sequence of operations changes the orientation in an incorrect way.

Step6: Check option E

Translating $\triangle AEF$ by the directed line segment from $F$ to $E$ and then rotating 180 degrees clockwise around point $E$ will not map it to $\triangle CFE$ as the combined operations do not align the triangles correctly.

Answer:

B. Rotate $\triangle AEF$ 180 degrees counter - clockwise around point $G$.
C. Rotate $\triangle AEF$ 180 degrees clockwise around point $G$.