Equidistant

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.