PLEASE HELP THIS IS DUE SOON AND I WAS SICK SO I NEED HELP. The preimage ∆ABC has points at A(2,-2), B(5,-4), and C(1,-6) and is dilated by a certain scale factor from a certain center of dilation. The image of ∆A'B'C' has points at A'(-6,8), B'(3,2), and C'(-9,-4). Use only algebraic reasoning (NO GRAPHING) to find the coordinates of the center of dilation. Show all work used below and provide a complete written justification for your answer. Explain what you did and why you did it.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?