In this scenario, since the lengths of the sides of the similar figure are twice the lengths of the corresponding sides of the original figure, the transformation involved is a dilation. A dilation changes the size of a figure while maintaining its shape and the proportions of its sides. In this case, the dilation factor is 2, meaning each point on the original figure is moved away from a center point (the center of dilation) by a factor of 2.
So, the correct response is dilation.