Investigating Matrix Transformations in the Cartesian Plane

Parameters a, b, c and d can be varied and are the elements of a matrix M. Points A, B, C and D are the vertices of a quadrilateral (set as the unit square but can be dragged) The matrix multiplication of M by the vertices of the quadrilateral is shown below.
Describe and classify the possible transformation. What is the effect of varying each parameter. What can you say about the matrix when the quadrilateral shrinks doen to a line segment?