Distance from a Point to a Line or Plane via Orthogonal Projection

This example demonstrates how the shortest distance from a point to a line or to a plane can be constructed visually using orthogonal lines and projections, with the ability to observe changes as inputs vary. Key concepts include the definition of point-to-line and point-to-plane distance, orthogonal projection, constructing perpendiculars (orthogonal lines), and locating intersection and foot of the perpendicular. The construction uses GeoGebra commands reflected in the provided command list: Textfield/Input boxes to set points and parameters (e.g., P, Q, plane), Line/Segment to create the geometric entities, OrthogonalLine to build perpendiculars from a point, ProjectPoint to obtain the projected (closest) point on the line/plane, Intersect to determine intersection points with planes/lines, Midpoint and Translate/Vector for supporting geometry and positioning, and Distance to measure and label the resulting distances (e.g., D, D_{plane}). It also leverages vector/coordinate-related objects (such as XandYline and coordinate parameters) to structure the visualization. Suitable for upper secondary through introductory university analytic/solid geometry instruction and interactive lesson demonstrations.