Quadrilateral abcd underwent a sequence of transformations to give quadrilateral a′b′c′d′. which transformations could not have taken place?

To maintain the same form, ergo, the same relative position between points A, B, C, and D, each of them have to be modified the same way, so speaking in coordinates, the following cannot happen:

A'-A ≠ B'-B ≠ C'-C ≠ D'-D
being A, A', B, B', and so on, the coordinates for each point.