Question

which of the following transformations carry this regular polygon onto itself? reflection across l rotation of 60° counterclockwise rotation of 72° clockwise rotation of 72° counterclockwise

Explanation:

Step1: Recall properties of regular hexagon

A regular hexagon has 6 - fold rotational symmetry and 6 lines of symmetry.

Step2: Analyze reflection

The line \(l\) is a line of symmetry of the regular hexagon. Reflection across a line of symmetry maps a figure onto itself.

Step3: Analyze rotation

The central angle of a regular hexagon is \(\frac{360^{\circ}}{6}=60^{\circ}\). A rotation of \(60^{\circ}\) counter - clockwise will map the hexagon onto itself. A rotation of \(72^{\circ}\) (clockwise or counter - clockwise) will not map the hexagon onto itself since \(360^{\circ}\div72^{\circ}=5\) and the hexagon has 6 - fold rotational symmetry.

Answer:

A. reflection across \(l\), B. rotation of \(60^{\circ}\) counterclockwise