Question

For the transformation to be defined as a rotation, which statements must be true? Choose three correct answers. Responses Every point on figure 1 moves through the same angle of rotation about the center of rotation, C , to create figure 2 . Every point on figure 1 moves through the same angle of rotation about the center of rotation, cap c , to create figure 2 . 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 segment connecting the center of rotation, cap 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 ). If figure 1 is rotated 180 ° about point C , it will be mapped onto itself. If figure 1 is rotated 180 degrees about point cap c , it will be mapped onto itself. The transformation is rigid. The transformation is rigid. Segment CP is parallel to segment CP ′ .

Answer 1

Step-by-step explanation:

For the transformation to be defined as a rotation, the following statements must be true:

1. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

2. 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).

3. If figure 1 is rotated 180 degrees about point C, it will be mapped onto itself.

Step-by-step explanation:

1. For a transformation to be considered a rotation, every point on figure 1 must move through the same angle of rotation about the center of rotation, C, to create figure 2. This means that each point maintains a fixed distance from the center and rotates in a circular path.

2. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) should have the same length as the segment connecting the center of rotation to its corresponding point on the image (figure 2). This ensures that the distances between the center of rotation and each point remain constant during the rotation.

3. If figure 1 is rotated 180 degrees about point C, it means that it is flipped over, and the resulting image will be identical to the original pre-image. This is because a rotation of 180 degrees brings each point back to its original position.

Therefore, the correct statements that must be true for the transformation to be defined as a rotation are:

- Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

- 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).

- If figure 1 is rotated 180 degrees about point C, it will be mapped onto itself.