Question

when reflecting the given preimage over the line y=x, is the image an isometry? yes, reflecting over the line y=x will create an isometry, but not all reflections do so. yes, all reflections maintain the same shape and size as the preimage. no, the image will be a different shape than the preimage.

Explanation:

An isometry is a transformation that preserves distance and shape. Reflections are rigid - motions, and all rigid - motions (translations, rotations, reflections) maintain the same shape and size as the pre - image. So, reflecting the preimage over the line \(y = x\) (which is a reflection) will result in an isometry.

Answer:

B. Yes, all reflections maintain the same shape and size as the preimage.