Question

select all the correct answers.
which rotations carry the square onto itself?
square image
□ 120° clockwise
□ 45° clockwise
□ 270° clockwise
□ 150° counterclockwise
□ 90° counterclockwise

Explanation:

Step1: Recall square rotation symmetry

A square has rotational symmetry of order 4, meaning it maps onto itself when rotated by multiples of \( \frac{360^\circ}{4}=90^\circ \) (clockwise or counterclockwise).

Step2: Check each option

• \( 120^\circ \) clockwise: Not a multiple of \( 90^\circ \), so no.
• \( 45^\circ \) clockwise: Not a multiple of \( 90^\circ \), so no.
• \( 270^\circ \) clockwise: \( 270^\circ = 3\times90^\circ \), multiple of \( 90^\circ \), yes.
• \( 150^\circ \) counterclockwise: Not a multiple of \( 90^\circ \), so no.
• \( 90^\circ \) counterclockwise: Multiple of \( 90^\circ \), yes.

Answer:

\( 270^\circ \) clockwise, \( 90^\circ \) counterclockwise (corresponding checkboxes should be selected: the option "270° clockwise" and "90° counterclockwise")