Question

what is true about every rotation?
the image is smaller than the pre - image.
the image is larger than the pre - image.
the corresponding lengths, from the point of rotation, between the pre - image and image are preserved.
the image is reduced or enlarged by a scale factor.

Explanation:

Rotation is a transformation that turns a figure around a fixed point (the center of rotation). One of the key properties of rotation is that it is a rigid transformation. Rigid transformations preserve the shape and size of the figure. This means that the distance from the center of rotation to any point in the pre - image is the same as the distance from the center of rotation to the corresponding point in the image.

• Option 1: Rotation does not change the size of the figure. So, the image is not smaller than the pre - image.
• Option 2: Rotation does not change the size of the figure. So, the image is not larger than the pre - image.
• Option 3: Since rotation is a rigid transformation, the corresponding lengths from the point of rotation (center of rotation) between the pre - image and image are preserved.
• Option 4: Rotation is not a dilation (a transformation that enlarges or reduces a figure by a scale factor).

Answer:

The corresponding lengths, from the point of rotation, between the pre - image and image are preserved.