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:

1. In a rotation, the distance from the center of rotation to a point on the pre - image is equal to the distance from the center of rotation to the corresponding point on the image because rotation is a rigid transformation that preserves distances.
2. Rotation is a type of rigid transformation which means that the shape and size of the figure remain the same.
3. All points on the pre - image rotate through the same angle about the center of rotation to form the image.
4. Segment CP and segment CP' are not parallel as there is a rotation involved.
5. There is no indication that figure 1 will map onto itself when rotated 180° about point C.

Answer:

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.