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:

Rotations are rigid transformations. Rigid transformations preserve shape and size (distance between points and angle measures). When a figure is rotated:

• Corresponding line segments have the same length.
• Corresponding angles have the same measure.
• Line segments connecting a point and its image after rotation are congruent. Let \(P\) be a point and \(P'\) be its image after rotation about center \(O\). Then \(OP = OP'\) (distance from center of rotation to a point and its image is the same).
• The angle between a point, the center of rotation, and its image is equal to the angle of rotation. For example, if the rotation angle is \(\theta\), then \(\angle POP'=\theta\).

Answer:

Rotations are rigid transformations. They preserve distances (lengths of line - segments) and angles. Line segments connecting a point and its image after rotation are congruent. The distance from the center of rotation to a point and its image is the same. The angle between a point, the center of rotation, and its image is equal to the angle of rotation.