Step 1 :Understand the properties of a perpendicular bisector: it divides a line segment into two equal parts and is perpendicular to the line segment.
Step 2 :If a point is on the perpendicular bisector of a segment, it should be equidistant from the endpoints of the segment.
Step 3 :\( \boxed{\text{Final Answer: B. equidistant from the endpoints of the segment}} \)