Question

example 1 identify transformations for symmetry try it! 1. a. what transformations map the figure onto itself?

Explanation:

Step1: Recall symmetry - type transformations

The main types of transformations are translations, rotations, reflections.

Step2: Analyze rotation for hexagon

A regular hexagon can be rotated by multiples of $\frac{360^{\circ}}{6}=60^{\circ}$ about its center to map onto itself. Rotations of $60^{\circ},120^{\circ},180^{\circ},240^{\circ},300^{\circ},360^{\circ}$ will work.

Step3: Analyze reflection for hexagon

A regular hexagon has 6 lines of symmetry. Reflection across any of these 6 lines will map the hexagon onto itself.

Answer:

Rotations by multiples of $60^{\circ}$ about its center and reflections across its 6 lines of symmetry.