Introduction
Sometimes it is necessary in geometry to specify the location of all points satisfying one or more conditions.
Locus of Point Equidistant from two given points
A locus of points is the set of points, and only those points, that satisfy given conditions - Every point satisfying the given conditions lies on the locus.
Theorem1
The locus of a point equidistant from two fixed points is the perpendicular bisector of the segment joining the two points.
Locus of Point Equidistant from two intersecting lines
The locus of points equidistant from the sides of a given angles is the bisector of the angle.
Theorem2
The locus of a point equidistant from two intersecting lines is the pair of lines bisecting the angles formed by the given lines.
Summary
The locus of points equidistant from two fixed points is the perpendicular bisector of the segment joining them.
