This conjecture is false, A and C don't have to be complementary angles.
Let Angle A be 100 and Angle B be 80 degrees. They are supplementary (sum of 180).
Let Angle C be 100 and Angle B is still 80 degrees. They are supplementary.
However, Angle A and Angle C are not complementary (sum of 90).
the translation takes the point A ( -1, -1) to (-1+4, 1) = (3, 1)
The refection in y = x 'flips' the points so (3, 1) becomes (1, 3) = A"
Do the same procedure for the other points to get the answer
(you should get B" = (-3, 3) )