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Dynamic Analysis - Descriptive Geometry

Dynamic Analysis - Descriptive Geometry
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2014-10-23 10:19
TriangleVectorCoordinate Geometry
In collections Complex Math
This example demonstrates the relationship of dynamic triangles, helping to visualize through descriptive geometry techniques. Key mathematical concepts include triangles, vectors, and coordinate geometry. Constructed using GeoGebra commands such as Vector, Point, Segment, etc. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Vector((5.17, 0), (7, 3)) → q
  2. Vector((1, 0), (1, 1)) → w
  3. Point(v) → A
  4. Point(u) → B_2
  5. Segment(A, B_2) → c
  6. Point(xAxis) → C
  7. Segment(A, C) → d
  8. Angle(C, A, B_2) → α
  9. OrthogonalLine(D, u, xOyPlane) → e
  10. Angle(c, e, xOyPlane) → β
  11. Point(c) → E
  12. Point(c) → F
  13. Point(d) → G
  14. Vector(H, I) → g
  15. Point(d) → A'
  16. Translate(B_2, g) → B'
  17. Segment(A', B') → c'
  18. Polygon(E, F, B', A') → poly1, e_1, f_1, b', a
  19. Vector(B', E) → h
  20. Vector(J, K) → i
  21. Translate(B_2, i) → B
  22. Vector(C, B) → j
  23. Vector(B, B_2) → k
  24. Vector(B, B') → l
  25. Mirror(A, c) → A'_1
  26. Dilate(j, 2, L) → j'
  27. Rotate(j', -90*°, B) → j''
  28. Dilate(j'', 0.25, L) → j'''
  29. Point(j''') → N
  30. Point(j') → M
  31. Vector(O, P) → p
  32. Translate(F, p) → F'
  33. Vector(Q, R) → r
  34. Translate(B, r) → S
  35. Vector(T, U) → s
  36. Translate(A, s) → A'_2
  37. Vector(V, W) → u_1
  38. Translate(S, u_1) → S'
  39. Vector(B, A') → m
  40. Vector(B_2, A') → n
  41. Point(c) → Z
  42. OrthogonalLine(Z, u) → t
  43. Line(Z, u) → a_1
  44. Rotate(a_1, 15*°, Z) → b_1
  45. Angle(c, t) → δ
  46. Vector(A_1, B_1) → v_1
  47. Translate(Z, v_1) → Z'
  48. Vector(Z, Z') → w_1
  49. Vector(C_1, D_1) → c_1
  50. Translate(Z, c_1) → Z'_1
  51. Vector(Z, Z'_1) → d_1
  52. Angle(c, a) → ε

AI Drawing Prompt Reference

This is a dynamic triangle analysis graphic that visualizes the relationship of dynamic triangles through descriptive geometry techniques. The graphic includes triangles, vectors, and coordinate geometry elements, along with multiple objects created through transformations like translation, rotation, and scaling. The construction order starts with vectors, then points, line segments, angles, and orthogonal lines, followed by transformations to generate new objects. The graphic aims to help understand the dynamic changes of triangles in coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.