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

Correct choices:
- The segment connecting the center of rotation, C, to a point on the pre-image is equal in length to the segment connecting C to the corresponding point on the image.
- The transformation is rigid.
- Every point on figure 1 moves through the same angle of rotation about C to create figure 2.

Reason: A rotation is an isometry (preserves distances = rigid) and every point rotates about the center through the same angle, so distances from the center before and after are equal. The other statements are not generally true (CP and CP' are not generally parallel; 180° rotation mapping the figure to itself is only true if the figure has 180° rotational symmetry).