Question

which of the following transformations carry this regular polygon onto itself? rotation of 60° clockwise reflection across ( l_1 ) rotation of 60° counterclockwise reflection across ( l_2 )

Explanation:

Step1: Properties of a regular hexagon

A regular hexagon has rotational symmetry of order 6. The angle of rotation for rotational symmetry is \(\frac{360^{\circ}}{n}\), where \(n = 6\) (number of sides). So, \(\frac{360^{\circ}}{6}=60^{\circ}\). A rotation of \(60^{\circ}\) clockwise or counter - clockwise will map the hexagon onto itself.

Step2: Reflection symmetry of a regular hexagon

A regular hexagon has 6 lines of symmetry. If \(l_1\) and \(l_3\) are lines of symmetry (by the nature of a regular hexagon's symmetry properties, a reflection across a line of symmetry will map the polygon onto itself).

Answer:

rotation of \(60^{\circ}\) clockwise, reflection across \(l_1\), rotation of \(60^{\circ}\) counterclockwise, reflection across \(l_3\)