Find the equation of the perpendicular bisector of the segment (e-1, 3-pi), (2-e, pi).

I found that the midpoint is (1/2, 3/2) and the slope of the perpendicular is (3-2e)/(-3+2pi). Substituting 1/2 and subtracting that from 3/2 would be difficult. Is there an easier way? Or did I make a mistake in my calculations?