To create a perpendicular bisector of a segment, it is a line drawn through the midpoint of the segment. Although one would immediately think that (A) would be the answer, just because a point is found on the perpendicular bisector, doesn't mean that it is immediately the midpoint. Although the midpoint is definitely found on the segment, there are numerous other points found on the segment. The midpoint is a point equidistant to both endpoints. Since the bisector passes through the midpoint, then any point on the bisector is equidistant to both endpoints. Therefore, the correct answer is B.