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.

Answer 1

Answers: 2, 3, and 6 are true. The others are false.

Short justifications:
- Rotations are always counterclockwise. — False. They can be clockwise or counterclockwise.
- Rotations preserve size. — True. Rotations are isometries: they preserve distances and angles.
- Rotations of 360° map a figure to itself. — True. A full turn sends every point back to its original position.
- Lines connecting corresponding points on the pre-image and image are parallel. — False. Those segments radiate from the center of rotation (they meet at the center), so they are generally not parallel.
- Lines connecting corresponding points on the pre-image and image have equal length. — False. The segment length between a point and its image depends on that point’s distance from the center (length = 2r·sin(θ/2)), so different points can give different lengths.
- Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length. — True. Rotation preserves distance from the center, so the center-to-point and center-to-image distances are equal.