The set of points that satisfy a given set of conditions.
In math, a locus (plural: loci) is a collection of points that all meet the same rule or condition. You can think of a locus as the path traced by a moving point that follows a certain rule.
For example:
- The set of all points that are the same distance from a single point forms a circle. That circle is a locus.
- The set of all points that are the same distance from two fixed points forms the perpendicular bisector of the segment connecting those two points.
Locus is an important concept in geometry, especially when studying shapes, distances, and constructions. It helps us describe and visualize paths, curves, and boundaries based on specific rules.
When Do Students Learn About Locus?
Students begin learning about the idea of loci when they explore distances and geometric constructions, often starting in middle school.
Grades 6–8 – Exploring Locus Through Geometry
Students are introduced to locus as a set of points that follow specific conditions, often through compass-and-straightedge constructions.
Grades 9+ – Using Locus in Advanced Geometry
Students use locus to solve more complex geometric problems, including conic sections and coordinate geometry.
