The endpoints of ab are a(0, 0) and b(6, 8)

a. describe a transformation of ab that results in the image whose endpoints are a'(8,4) and b'(-2, 4) .

b. what are the endpoints of the image of a'b' after a dilation whose scale factor is 4/5 and whose center is a' ?

c. what quadrant does a' lie in?

We are given the endpoints. We are also given the endpoints after the transformation. For the first item, a simple distance formula verification would reveal that the distance between AB and A'B' is not equal. So, a dilation must have been done. Next, AB and A'B' are not parallel which means that a translation transformation must have been done.
After a dilation of 4/5 with A as the center, A' is still (0,0) and B' is (6 - 24/5, 8 - 32/5).