The transformations rotation, reflection and translation don't modify the lengths of the sides of the quadrilateral. This means that any of these transformations preserve all the features of quadrilateral ABCD. Then, under these transformations, the quadrilaterals are congruent.
When the transformation is a dilation, then the mapped quadrilateral will have its sides changed, and because of that, the mapped quadrilateral is not congruent with the original figure.
Therefore, the transformation that would not result in the two quadrilaterals being congruent is the dilation from point A by a factor of one half (option B)