Question

Any point on the perpendicular bisector of a segment is equidistant to the endpoints of that segment

Answer 1

Let it be:

Line segment AB, C is its perpendicular bisector, wich means that it cuts the line segment in exact haves trough point M (midpoint).

Then the distance of any point in the perpendicular line C is midway between A and B, i.e. it is equidistant to the endpoints.

Therefore, the statement is true.