The perpendicular bisector as a locus

Remark

The perpendicular bisector of a segment with endpoints $A$ and $B$ is the locus of the points of the plane that are equidistant from $A$ and from $B$: $P \in a \iff d(P, A) = d(P, B).$ Geometrically it is the line perpendicular to the segment passing through its midpoint.

Links

Topics: Loci
Concepts: Perpendicular bisector of a segment · Distance between points · Locus · Cartesian plane
Skills: Analytic geometry