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Reflection About a Plane

Reflection About a Plane
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2017-11-24 09:24
Solid GeometryTransformationGeometric Construction
This example illustrates the reflection about a plane. Key mathematical concepts include reflection, mirroring, and plane geometry. Using GeoGebra commands such as Plane, Mirror, Segment, and Intersect, the reflection process is dynamically demonstrated. Suitable for high school geometry and solid geometry education.

GeoGebra Commands & Parameters

  1. Plane(B, C, A) → a
  2. Pyramid(E, D, F, G) → b, faceDEF, edgeFG, faceDEG, faceDFG, faceEFG, edgeDE, edgeDF, edgeEF, edgeEG, edgeDG
  3. Mirror(b, a) → b'
  4. Mirror(D, a) → D'
  5. Mirror(E, a) → E'
  6. Mirror(G, a) → G'
  7. Mirror(E, a) → E'_1
  8. Mirror(D, a) → D'_1
  9. Segment(E'_1, D'_1) → edgeDE'
  10. Mirror(D, a) → D'_2
  11. Mirror(F, a) → F'
  12. Segment(D'_2, F') → edgeDF'
  13. Mirror(D, a) → D'_3
  14. Mirror(G, a) → G'_1
  15. Segment(D'_3, G'_1) → edgeDG'
  16. Mirror(F, a) → F'_1
  17. Mirror(E, a) → E'_2
  18. Segment(F'_1, E'_2) → edgeEF'
  19. Mirror(G, a) → G'_2
  20. Mirror(E, a) → E'_3
  21. Segment(G'_2, E'_3) → edgeEG'
  22. Mirror(F, a) → F'_2
  23. Mirror(G, a) → G'_3
  24. Segment(F'_2, G'_3) → edgeFG'
  25. Line(F, F'_2) → f
  26. Line(G, G'_2) → g
  27. Line(D, D') → h
  28. Line(E, E') → i
  29. Intersect(f, a) → H
  30. Angle(F, H, B) → α
  31. Dilate(F, If[0 < e ≤ 1, 1 - e, 0], H) → F'_3
  32. Segment(F, F'_3) → j
  33. Dilate(H, If[1 < e ≤ 2, 2 - e, 0], F'_2) → H'
  34. Segment(H, H') → k
  35. Plane(H, C, F'_2) → l
  36. Rotate(F, If[2 < e ≤ 3, ((e - 2) * π), π], H, l) → F'_4
  37. Rotate(F'_3, If[2 < e ≤ 3, ((e - 2) * π), π], H, l) → L
  38. Segment(F'_4, L) → j'
  39. Dilate(B, If[0 < e ≤ 1, 1 - e, 0], H) → B'
  40. Segment(B, B') → m
  41. Line((0, 0, 0), (1, 0)) → p
  42. Line((0, 0, 0), (0, 1, 0)) → q
  43. Line((0, 0, 0), (0, 0, 1)) → r