The coordinates of δabc are (-3, 4), (0, 4), and (2, 5). the coordinates of δa'b'c' are (-1.5, 2), (0, 2) and (1, 2.5). how do you know that the transformation is a dilation?

Any transformation that is getting smaller is a dilation.  Bigger, an enlargment.  In this instance, it is a scale factor of 1/2, because scale factor 1 is congruent, greater than one an enlargement, less than one but greater than zero is a dilation.

Whose mistake? can you give more details to what the question is asking?