Question

figure 2 was constructed using figure 1. for the transformation to be defined as a rotation, which statements must be true? select three options. the segment connecting the center of rotation, c, to a point on the pre - image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2). the transformation is rigid. every point on figure 1 moves through the same angle of rotation about the center of rotation, c, to create figure 2. segment cp is parallel to segment cp. if figure 1 is rotated 180° about point c, it will be mapped onto itself.

Explanation:

Step1: Property of rotation

In a rotation, the distance from the center of rotation to a point on the pre - image and its corresponding point on the image is the same. Mathematically, if \(P\) is a point on the pre - image and \(P'\) is its image after rotation about a center \(C\), then \(CP = CP'\).

Step2: Rigid transformation

A rotation is a rigid transformation. Rigid transformations preserve distance and angle measures. So, the shape and size of the figure remain the same after rotation.

Step3: Angle of rotation

For a rotation about a center \(C\), every point on the pre - image rotates through the same angle about \(C\) to form the image. This is a fundamental property of rotation.

Step4: Analyze non - correct options

Segment \(CP\) is not parallel to segment \(CP'\) in general for a non - zero rotation. And just because figure 1 is rotated \(180^{\circ}\) about point \(C\) does not mean it will be mapped onto itself (it depends on the symmetry of figure 1).

Answer:

• A. The segment connecting the center of rotation, C, to a point on the pre - image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
• B. The transformation is rigid.
• C. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.