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Descriptive Geometry

Descriptive Geometry
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2019-12-16 03:04
VectorCoordinate GeometrySolid GeometryTransformationGeometric Construction
This example demonstrates basic geometric construction methods in descriptive geometry. The core math concepts involved include vectors, points, segments, angles, orthogonal lines, translation, polygons, reflection, dilation, rotation, etc. Construction highlights involve using commands and objects like Vector, Point, Segment, Angle, OrthogonalLine, Translate, Polygon, Mirror, Dilate, Rotate, Line, Textfield in GeoGebra. Suitable for high school and above students to learn geometric construction techniques.

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
  53. Textfield(Σ) → InputBox1
  54. Point(b') → G_1
  55. Line(G_1, b') → f_2
  56. Angle(f_2, a) → ζ
  57. Point(e) → H_1
  58. Point(s_1) → I_1
  59. Segment(H_1, I_1) → g_2
  60. Angle(g_2, e, xOyPlane) → θ

AI Drawing Prompt Reference

Draw a geometric figure that includes vectors and points, demonstrating basic construction methods. Start by creating two vectors, then form points based on the first vector and connect them to create a line segment. Next, use points on the coordinate axes and vectors to perform transformations like translation, rotation, reflection, and dilation, creating multiple polygons and geometric objects. Finally, complete the construction using angles and orthogonal lines, showcasing fundamental geometric concepts such as vectors, points, line segments, and polygons.
The prompt above was compiled from the original drawing commands and is for reference only.