Question

which of the following transformations carry this regular polygon onto itself? rotation of 90° clockwise rotation of 120° counterclockwise rotation of 45° counterclockwise reflection across l

Explanation:

Step1: Recall rotation symmetry of a square

A square has a rotation symmetry of \(90^{\circ}\). When rotated \(90^{\circ}\) clockwise or counter - clockwise, it maps onto itself.

Step2: Check rotation angles

For a square, the angle of rotation that maps it onto itself is \(\frac{360^{\circ}}{n}\), where \(n = 4\) (number of sides). \(\frac{360^{\circ}}{4}=90^{\circ}\). Rotations of \(120^{\circ}\) and \(45^{\circ}\) do not map a square onto itself as \(120^{\circ}\) and \(45^{\circ}\) are not factors of \(360^{\circ}\) in the context of a square's rotation symmetry.

Step3: Recall reflection symmetry

A square has reflection symmetry. If the line \(l\) is a line of symmetry (in this case, a horizontal line of symmetry for the square shown), a reflection across \(l\) will map the square onto itself.

Answer:

rotation of \(90^{\circ}\) clockwise, reflection across \(l\)