Question

which are properties of rotations? check all that apply
rotations are always counterclockwise
rotations preserve size
rotations of 360° map a figure to itself
lines connecting corresponding points on the pre - image and image are parallel
lines connecting corresponding points on the pre - image and image have equal length
lines connecting the center of rotation to the pre - image and the corresponding point on the image have equal length

Explanation:

Step1: Analyze rotation direction

Rotations can be clockwise or counter - clockwise. So, “Rotations are always counter - clockwise” is wrong.

Step2: Check size preservation

Rotation is a rigid transformation. Rigid transformations preserve the size and shape of the figure. So, “Rotations preserve size” is correct.

Step3: Consider \(360^{\circ}\) rotation

A rotation of \(360^{\circ}\) means a full - turn. A full - turn rotation maps a figure onto itself. So, “Rotations of \(360^{\circ}\) map a figure to itself” is correct.

Step4: Examine lines between corresponding points

Lines connecting corresponding points on the pre - image and image are not necessarily parallel. For example, a non - \(180^{\circ}\) rotation of a non - symmetric figure. So, “Lines connecting corresponding points on the pre - image and image are parallel” is wrong.

Step5: Analyze lengths of lines between corresponding points

Lines connecting corresponding points on the pre - image and image do not have to have equal length. But lines connecting the center of rotation to the pre - image and the corresponding point on the image (by the definition of rotation, which is a circular motion around a center) have equal length. So, “Lines connecting corresponding points on the pre - image and image have equal length” is wrong and “Lines connecting the center of rotation to the pre - image and the corresponding point on the image have equal length” is correct.

Answer:

• Rotations preserve size
• Rotations of \(360^{\circ}\) map a figure to itself
• Lines connecting the center of rotation to the pre - image and the corresponding point on the image have equal length