Perpendicular bisector to a segment (GMT)

Given a segment $AB$, its perpendicular bisector is the line that passes through the midpoint $M$ of $AB$ and is perpendicular to $AB$. Every point on this line is equidistant from $A$ and $B$.

Important properties

• The perpendicular bisector divides the segment into two equal parts.

• It forms a right angle (90°) with the segment.

• Any point on the perpendicular bisector is the same distance from both endpoints of the segment.

• The perpendicular bisector is a locus: the set of all points equidistant from $A$ and $B$.