In the scenario you presented, since the lengths of the sides of the similar figure are twice the lengths of the corresponding sides of the original figure, a dilation is the necessary transformation that must occur.
Dilation is a transformation that changes the size of a figure but preserves its shape, by expanding or contracting it based on a scale factor. In this case, the scale factor is 2, meaning the image is twice as large as the original figure.
So, the correct response is dilation.