Question

select the correct answer.
which property of a rigid transformation is exclusive to rotations?
a. the measures of the angles and sides in the preimage are preserved.
b. a line segment connecting the image to the preimage forms a 90° angle with the center of rotation.
c. the distance from each point on the image to the center of rotation is preserved.
d. all the points on the image move along a parallel line when the preimage is transformed.

Explanation:

• Option A: Both translations and rotations preserve the measures of angles and sides. So this is not exclusive to rotations.
• Option B: A line - segment connecting the image to the pre - image forms a \(90^{\circ}\) angle with the center of rotation is not a general property of rotations. Rotations can be by any angle (\(\theta

eq90^{\circ}\) is also possible).

• Option C: In a rotation, the distance from each point on the pre - image to the center of rotation is the same as the distance from the corresponding point on the image to the center of rotation. This is a unique property of rotations among rigid transformations (translations do not have a center of rotation with this distance - preservation property related to a center).
• Option D: When there is a rotation, points move along circular paths (not parallel lines as in translations).

Answer:

C. The distance from each point on the image to the center of rotation is preserved.