Geometric loci

In solid geometry, a geometric locus is the set of all points in three-dimensional space that satisfy a given geometric condition. For example, the locus of points equidistant from two fixed points is the perpendicular bisector plane of the segment joining those points.

Important properties

• A locus can be a point, line, plane, surface, or more complex shape.

• The condition defining the locus must be clearly stated and can involve distances, angles, or other geometric relationships.

• Common loci in space include spheres (fixed distance from a point), planes (fixed distance from a plane or line), and lines (intersection of two planes).