Question

which are properties of rotations? check all that apply.

rotations are always counterclockwise.
rotations preserve size.
rotations of \\(360^\circ\\) 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:

Analyze definition and direction of rotations

Rotations can be clockwise or counterclockwise.
Rotations are rigid transformations, which preserve size and shape.
A full rotation of \(360^\circ\) returns any figure to its original position.

Analyze line segments between pre-image and image points

Lines connecting corresponding points on the pre-image and image are not generally parallel (they lie on concentric circles).
The distances between corresponding pre-image and image points vary depending on their distance from the center of rotation.

Analyze distance to the center of rotation

By definition, every point and its rotated image lie on a circle centered at the center of rotation.
Thus, the distance from the center of rotation to a pre-image point equals the distance from the center of rotation to the corresponding image point.

Answer:

• Rotations are always counterclockwise.
• Rotations preserve size. (Correct answer)
• Rotations of 360° map a figure to itself. (Correct answer)
• 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. (Correct answer)