What a locus is

A locus is a way of describing a figure not through its shape, but through a property that its points — and only they — possess.

Definition — Locus

A locus is the set of all and only the points that enjoy a certain property.

• All: every point with that property belongs to the locus (a sufficient condition).
• Only: only points with that property belong to the locus (a necessary condition).

The two most important loci of the plane are the perpendicular bisector of a segment and the bisector of an angle.

Property — Perpendicular bisector and angle bisector as loci

• The perpendicular bisector of a segment is the locus of the points equidistant from the endpoints.
• The bisector of an angle is the locus of the points equidistant from the two sides.

On the left: the points of the perpendicular bisector are equidistant from the endpoints $A$ and $B$. On the right: the points of the bisector are equidistant from the two sides of the angle.

Links

Topics: Euclidean geometry
Concepts: Perpendicular bisector of a segment · Angle bisector · Locus
Skills: Synthetic geometry