Question

Figure 2 was constructed using figure 1.

On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0). Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

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.

Answer 1

Select the first, second, and third statements.

- The segment from the center C to a point and to its image have equal length. (Rotations preserve distance from the center.)
- The transformation is rigid. (Rotations are isometries — they preserve lengths and angles.)
- Every point on the preimage moves through the same angle about C to form the image. (All points rotate by the same angle around the center.)

The other two statements are not generally true for a rotation.