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Closest Point Construction

Closest Point Construction
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2019-11-15 10:40
VectorCoordinate GeometryTransformationGeometric Construction
In collections Exploring Orthogonality
This example demonstrates the construction of the closest point from a point to a plane in three-dimensional space. The core mathematical concepts involved include planes, orthogonal lines, points, intersections, segments, and angles. The construction utilizes GeoGebra commands such as Plane, OrthogonalLine, PointIn, Intersect, Segment, and Angle, along with objects like A, B, C, a, x_0, f, w, w_0, g, h, i, α, text2, and text1. It is suitable for high school and above learning spatial geometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Plane(A, C, B) → a
  2. OrthogonalLine(x_0, a) → f
  3. PointIn(a) → w
  4. Intersect(f, a) → w_0
  5. Segment(w, w_0) → g
  6. Segment(w, x_0) → h
  7. Segment(x_0, w_0) → i
  8. Angle(x_0, w_0, w) → α

AI Drawing Prompt Reference

In 3D space, construct a plane through three non-collinear points. From a point outside the plane, draw a perpendicular line to the plane, intersecting it at a foot point. Connect the outside point to the foot point with a segment. Then choose an arbitrary point on the plane, and connect it to both the foot point and the outside point, forming a triangle. Finally, mark the angle at the foot point between the outside point and the arbitrary point on the plane, and display its measure.
The prompt above was compiled from the original drawing commands and is for reference only.