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, shape, and size. Reflection is a type of isometry. When a pre - image is reflected over any line (including y = x), the resulting image has the same shape and size as the pre - image.

Answer:

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