Locus Reference Sheet:
A locus in a plane is the set of all points in a plane that satisfy a given condition or a set
of given conditions. The word locus is derived from the Latin word for “location.” The
plural of locus is loci, pronounced “low-sigh.”
There are five basic loci: points at a set distance from a fixed point, points equidistant
from parallel lines, and points equidistant from intersecting lines.
Locus Theorem 1: Distance From a Point: The Circle
The locus at a fixed distance from a given point is a circle.
Example:
Locus Theorem 2: Equidistant From Two Points: The Perpendicular Bisector
The locus equidistant from two points is a perpendicular bisector.
Example:
Locus Theorem 3: Distance From a Line: Two Parallel Lines
The locus at a fixed distance from a line is a set of two parallel lines.
Example:
Locus Theorem 4: Equidistant From Two Parallel Lines: One Parallel Line
The locus equidistant from two parallel lines is a line parallel to the lines and midway
between them.
Example:
Locus Theorem 5: Equidistant From Intersecting Lines: The Angle Bisector
The locus equidistant from two intersecting lines is the bisectors of each pair of vertical
angles formed by the lines.
Example: