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Distance Between Points and Lines or Planes

Distance Between Points and Lines or Planes
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2016-08-31 06:12
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to calculate the distance between a point and a line or a plane. It involves core mathematical concepts such as vectors, projection, coordinate geometry, and the cosine theorem. Key GeoGebra commands and objects used include Textfield, Translate, Vector, Distance, OrthogonalLine, Intersect, Midpoint, Line, Segment, Angle, ProjectPoint, XandYline. Suitable for high school and above students to learn spatial geometry and coordinate geometry problems.

GeoGebra Commands & Parameters

  1. Textfield(P) → InputBox1
  2. Textfield(n) → InputBox2
  3. Translate(P, n) → P'
  4. Vector(P, P') → u
  5. Textfield(Q) → InputBox3
  6. Vector(P, Q) → v
  7. Distance(Q, plane) → D_{plane}
  8. OrthogonalLine(Q, plane) → f
  9. Intersect(f, plane) → D
  10. Vector(D, Q) → w
  11. Midpoint(D, Q) → E
  12. Line((x(P), y(P), z(P)), Vector[(x(n), y(n), z(n))]) → line
  13. OrthogonalLine(Q, line, space) → g
  14. Intersect(line, g) → M
  15. Segment(M, Q) → h
  16. Midpoint(h) → N
  17. Angle(P', P, Q) → α
  18. ProjectPoint(Q) → A, l
  19. ProjectPoint(P) → B, m
  20. XandYline(B) → p, q
  21. XandYline(A) → r, s
  22. Segment(F, G) → t