Question

which of the following transformations carry the rectangle onto itself?
rotation of 90°
clockwise
rotation of 180°
clockwise
rotation of 45°
counterclockwise
rotation of 90°
counterclockwise

Explanation:

Step1: Recall the properties of rectangle rotation

A rectangle has rotational symmetry of order 2. That means a rotation of \(180^{\circ}\) (either clockwise or counter - clockwise) about its center will map the rectangle onto itself.
A rotation of \(90^{\circ}\) (clockwise or counter - clockwise) will not map a non - square rectangle onto itself. Because the length and width of a non - square rectangle are different. After a \(90^{\circ}\) rotation, the position of the length and width (which are not equal) will change, so the rectangle will not coincide with the original one.
A rotation of \(45^{\circ}\) (counter - clockwise) will also not map the rectangle onto itself. Since the angles and side - length ratios of a rectangle do not match the requirements for a \(45^{\circ}\) rotational symmetry.

Answer:

rotation of \(180^{\circ}\) clockwise