Among the given options, only a dilation followed by a rotation would produce an image that is not congruent to its pre-image.
A translation simply shifts the pre-image to a new location without changing its size or shape, resulting in a congruent image.
A reflection creates a mirror image of the pre-image, which is also congruent to the pre-image.
A rotation of 90 degrees about the origin rotates the pre-image but maintains its size and shape, making the resulting image congruent to the pre-image.
However, a dilation followed by a rotation changes both the size and shape of the pre-image, producing an image that is not congruent to the pre-image.
The dilation alters the size of the pre-image, and the subsequent rotation further disrupts its shape, resulting in a non-congruent image.