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GeoGebra 3D Geometric Transformation Exercise 42

GeoGebra 3D Geometric Transformation Exercise 42
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2021-09-02 17:48
VectorSolid GeometryComplex NumberTransformationGeometric Construction
This example demonstrates complex geometric transformations in three dimensions, involving concepts such as vectors, geometric transformations, and complex numbers. The construction requires using GeoGebra commands like Polygon, PointIn, Segment, Rotate, Prism, Vector, Point, Angle, and Midpoint, along with creating faces and edges. Steps include defining points A, B, C, D, etc., then applying rotation and prism operations to generate 3D figures. Suitable for high school students or college undergraduates learning 3D geometry and vector applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → q1, a, b, d, c
  2. PointIn(Sphere[C, 2.25]) → G
  3. Segment(C, G) → g
  4. Rotate(G, 135°, c) → G'
  5. Prism(C, D, B, A, G') → e, E, edgeCD_{1}, edgeBD_{1}, edgeAB_{1}, edgeAC_{1}, edgeCG', edgeDE, edgeBF, edgeAH, edgeEG', edgeEF, F, edgeFH, edgeG'H, H, faceABDC_{1}, faceCDEG', faceBDEF, faceABFH, faceACG'H, faceEFHG'
  6. Segment(A, B) → f
  7. Segment(B, D) → h
  8. Segment(E, D) → i
  9. Segment(F, B) → j
  10. Segment(H, A) → k
  11. Segment(H, F) → l
  12. Segment(F, E) → m
  13. Segment(E, G') → n
  14. Segment(H, G') → p
  15. Vector(C, A) → u
  16. Vector(C, G') → v
  17. Vector(C, D) → w
  18. Point(i) → I
  19. Prism(D, B, A, C, I) → o, J, edgeBD, edgeAB, edgeAC, edgeCD, edgeDI, edgeBJ, edgeAK, edgeCL, edgeIJ, edgeJK, K, edgeKL, edgeIL, L, faceABDC, faceBDIJ, faceABJK, faceACLK, faceCDIL, faceIJKL
  20. Vector(C, M) → q
  21. Angle(G', C, M) → α
  22. Midpoint(C, A) → N
  23. Midpoint(C, G') → O
  24. Midpoint(C, D) → P

AI Drawing Prompt Reference

Create a 3D geometric transformation example. Start by defining a quadrilateral base in space. Then take a point on the base, rotate it 135 degrees around one edge of the quadrilateral to obtain a new vertex, and create a prism using this vertex and the base. Next, pick a point on one of the lateral edges of the first prism, and create a second prism using the same base and this point. The diagram shows two intersecting prisms in space with connections between vertices, vectors, and midpoint relationships marked.
The prompt above was compiled from the original drawing commands and is for reference only.