Question

which of the following transformations carry this regular polygon onto itself? rotation of 72° clockwise rotation of 90° clockwise rotation of 60° counterclockwise reflection across l

Explanation:

Step1: Identify the polygon

The figure is a regular hexagon. A regular hexagon has 6 sides.

Step2: Determine rotational symmetry

The central angle for a regular hexagon is $\frac{360^\circ}{6} = 60^\circ$. So a rotation by a multiple of $60^\circ$ (clockwise or counterclockwise) will map the hexagon onto itself. Also, reflection across a line of symmetry (like line \( l \) which seems to pass through midpoints of opposite sides or vertices) will map it onto itself.

• Rotation of \( 72^\circ \): Not a multiple of \( 60^\circ \), so incorrect.
• Rotation of \( 90^\circ \): Not a multiple of \( 60^\circ \), so incorrect.
• Rotation of \( 60^\circ \) counterclockwise: Multiple of \( 60^\circ \), so correct.
• Reflection across \( l \): Line \( l \) is a line of symmetry (since it passes through midpoints of two opposite sides in a regular hexagon), so reflection across \( l \) is correct.

Answer:

rotation of \( 60^\circ \) counterclockwise, reflection across \( l \)