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2.8 Simetría con deslizamiento: 3D Vector and Transformation Geometry

2.8 Simetría con deslizamiento: 3D Vector and Transformation Geometry
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2023-03-22 20:36
VectorTransformationGeometric Construction
In collections geometriadinamica.es
This example demonstrates the geometric construction of vector transformations and distance calculations in three-dimensional space. Key mathematical concepts include vector operations, mirror transformations, and distance formulas. The construction involves using GeoGebra commands such as Line, Circle, Intersect, OrthogonalLine, Point, LineBisector, Ray, Vector, Length, Mirror, Translate, etc. It is suitable for high school students or college undergraduates learning 3D geometry transformations and vector applications.

GeoGebra Commands & Parameters

  1. Line(A, B) → b
  2. Circle(A, d1) → d
  3. Circle(B, d1) → e
  4. Intersect(d, b, 2) → C
  5. Intersect(e, b, 1) → D
  6. OrthogonalLine(A, b) → f
  7. OrthogonalLine(B, b) → g
  8. Point(f) → E
  9. OrthogonalLine(E, f) → h
  10. Intersect(g, h) → F
  11. Circle(E, d1) → k
  12. Circle(F, d1) → p
  13. Intersect(k, h, 1) → G
  14. LineBisector(E, F) → i
  15. Ray(A, D) → j
  16. Intersect(d, j) → I, N
  17. Intersect(e, j, 2) → J
  18. Ray(D, A) → l
  19. Intersect(e, l) → K, L
  20. OrthogonalLine(D, b) → m
  21. Intersect(b, i) → H
  22. Line(M, i) → n
  23. Point(n) → O
  24. Vector(M, O) → u
  25. Length(u) → l1
  26. Min(l1, (l1 * (a - 1.5))) → dd
  27. Mirror(pic1, i) → pic1'
  28. Line(P, u) → q
  29. Circle(P, dd) → r
  30. Intersect(r, q, 2) → Q
  31. Vector(P, Q) → w
  32. Translate(pic1', w) → pic1''
  33. OrthogonalLine(M, u) → s
  34. Point(i) → R
  35. CircleArc(R, A, B) → t
  36. OrthogonalLine(C, b) → a_1
  37. Intersect(t, a_1, 1) → S
  38. Mirror(S, H) → S'

AI Drawing Prompt Reference

Create a geometric construction demonstrating glide symmetry with 3D vector transformations. Start by establishing a baseline line and marking two points on it, then draw circles with equal radius centered at these points and find their intersections with the line. Construct perpendicular lines from these intersection points to the baseline, pick points on the perpendiculars and draw additional circles. Connect corresponding points to create perpendicular bisectors. Generate a mirror image of the figure across the bisector, then apply vector translation to achieve the glide symmetry effect. Include rays, circular arcs, and perpendicular lines throughout the construction to show the complete geometric transformation relationship.
The prompt above was compiled from the original drawing commands and is for reference only.