Distance from Points to Lines and Planes in 3D

This GeoGebra example demonstrates the perpendicular distance from a point to a line and from a point to a plane in three-dimensional space, combining geometric construction with algebraic computation. Core mathematical concepts include analytic geometry, vector projection, orthogonal projection, point-to-line distance formula, and point-to-plane distance formula. The construction uses GeoGebra commands such as Textfield, Translate, Vector, Distance, OrthogonalLine, Intersect, Midpoint, Line, ProjectPoint, XandYline, and Segment, together with objects P, Q, plane, line, normal vector n, direction vector v, and distance values D_plane and D to build an interactive model. It is suitable for high school analytic geometry and solid geometry instruction, as well as college-level preparatory courses in vector geometry before calculus, supporting classroom demonstrations and independent student exploration.