Question

describe the general properties of rotations. include a discussion of the properties of rigid transformations, and line segments connecting corresponding points to each other and to the center of rotation.

Explanation:

A rotation is a rigid transformation. Rigid transformations preserve shape and size. So, in a rotation, the pre - image and image are congruent.
For the line segments connecting corresponding points:

• The line segments connecting corresponding points are congruent. Let \(P\) be a point in the pre - image and \(P'\) be its image after rotation. Then \(PP'\) has the same length for all pairs of corresponding points.
• The line segments connecting corresponding points are related to the center of rotation \(O\). The center of rotation \(O\) is equidistant from a point \(P\) and its image \(P'\), i.e., \(OP = OP'\). Also, the angle between \(OP\) and \(OP'\) is equal to the angle of rotation.

Answer:

A rotation is a rigid transformation. The pre - image and image are congruent. Line segments connecting corresponding points are congruent. The center of rotation is equidistant from a point and its image, and the angle between the line segments from the center of rotation to a point and its image is equal to the angle of rotation.