Question

select all sequences of translations
a rotate 180° around point a.

b translate so that a is taken to j. then reflect over line ba

c rotate 60°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:

To determine the correct sequences, we analyze each option:

• Option A: Rotating 180° around A might not align with the intended transformation (likely involving a 60° rotation context, e.g., equilateral triangle - like structure). So A is incorrect.
• Option B: Translating A to J then reflecting over BA doesn't match the typical symmetry (e.g., 60° rotations in a triangular grid). Incorrect.
• Option C: Rotating 60° counterclockwise around A then reflecting over FA. In a 60° - based (equilateral) setup, this sequence may not work. Incorrect.
• Option D: Reflecting over BA then rotating 60° counterclockwise around A. In a triangular (60° angle) context, this sequence can map the figure correctly (e.g., for a triangle with vertex A, reflecting then rotating 60° to align). Correct.
• Option E: Reflecting over BA then translating by EA. Translation here doesn't fit the rotational symmetry. Incorrect.

Answer:

D. Reflect over the line BA and then rotate \( 60^\circ \) counterclockwise around point A.