Library/Geometry/Solid geometry/Geometric loci/GMT in space (other)

GMT in space (other)

Overview
Important

In three-dimensional (3D) geometry, a geometric locus is the set of all points in space that satisfy a certain condition or a set of conditions. Problems involving loci in space often ask you to describe or find the shape or equation of all points that are a fixed distance from a point, a line, a plane, or satisfy other geometric constraints.

Important properties

  • The locus of points at a fixed distance from a point in space is a sphere.

  • The locus of points equidistant from two points is a plane (the perpendicular bisector plane).

  • The locus of points equidistant from two parallel planes is another plane halfway between them.

  • The locus of points equidistant from two intersecting planes is a plane that bisects the dihedral angle between them.

  • Loci in space can be described using vector equations or Cartesian equations.