It's a high school trig problem. Originally ABC were on a line. A' is 1/8' (we assume at a right angle to the original ABC line. If A' is 1/8" along the original ABC line then B does not move. No matter what we need to know the angle of A' vs the original ABC line.
Then the new line is A'C. The problem to be solved is the location of B' (where the new line is A'B'C.
It ought the be a solution for a right angle triangle.
But we need to know the precise location of A' first.
If this is a theoretical problem where all of them are zero dimensioned points there will be an answer. if this is a practical problem then just overdrill the f'n hole at B' and get over it. A bolt and washer washer will cover it.
If you need an engineer stamped drawing find a PE.