the answer:
the complement of the question is as follow
What is the scale factor of the dilation?
when we look at the image,
UV and U'V' are parallels, and (A, U V) and (A, U' V') are aligned points
so we can apply thales theorem
AV/AV' = AU / AU'= VU /V'U'= 3.2+4.8/ 3.2= 8/3.2
so VU / V'U'= 8/3.2, the image is formed by a reduction
VU = 8/3.2 V'U', so k=8/3.2
the scale factor of the dilation is k=8/3.2
