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Rectangle Construction by youngcar

Rectangle Construction by youngcar
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2017-12-12 14:41
Coordinate GeometryTransformationGeometric Construction
This example demonstrates how to construct a rectangle using GeoGebra. It involves core mathematical concepts such as straight lines, orthogonal lines, points, intersections, polygons, circles, rotations, and reflections. Key construction steps include using Segment to draw segments, OrthogonalLine to create perpendicular lines, Point to place points, Intersect to find intersections, Polygon to form polygons, Circle to draw circles, Line to create lines, Rotate for rotations, and Mirror for reflections. Suitable for high school mathematics education to understand geometric constructions and transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, b) → d
  6. Intersect(c, d) → D
  7. Polygon(C, D, B, A) → poly1, c_1, d_1, b_1, a_1
  8. Segment(C, B) → e
  9. Segment(D, A) → f
  10. Intersect(e, f) → E
  11. Segment(K, L) → l
  12. Circle(K, L) → p
  13. Point(p) → M
  14. Segment(K, M) → m
  15. Line(M, l) → n
  16. Line(L, m) → q
  17. Intersect(n, q) → N
  18. Segment(M, L) → r
  19. Segment(N, K) → s
  20. Intersect(r, s) → O
  21. Rotate(C, (-α), E) → C'
  22. Rotate(D, (-α), E) → D'
  23. Rotate(B, (-α), E) → B'
  24. Rotate(A, (-α), E) → A'
  25. Polygon(C', D', B', A') → poly1', c', d', b', a'
  26. Rotate(M, (-α), O) → M'
  27. Rotate(N, (-α), O) → N'
  28. Rotate(L, (-α), O) → L'
  29. Rotate(K, (-α), O) → K'
  30. Polygon(M', N', L', K') → poly3', m', n', l', k'
  31. Segment(P, Q) → t
  32. Segment(P, R) → e_1
  33. Line(Q, e_1) → g_1
  34. Line(R, t) → h_1
  35. Intersect(g_1, h_1) → S
  36. Segment(R, Q) → i_1
  37. Segment(S, P) → j_1
  38. Intersect(i_1, j_1) → T
  39. Rotate(P, (-α), T) → P'
  40. Rotate(R, (-α), T) → R'
  41. Rotate(S, (-α), T) → S'
  42. Rotate(Q, (-α), T) → Q'
  43. Segment(U, V) → t_1
  44. Line(W, t_1) → b_2
  45. Point(b_2) → Z
  46. Segment(W, V) → d_2
  47. Segment(Z, U) → e_2
  48. Intersect(d_2, e_2) → A_1
  49. Rotate(U, (-α), A_1) → U'
  50. Rotate(V, (-α), A_1) → V'
  51. Rotate(Z, (-α), A_1) → Z'
  52. Rotate(W, (-α), A_1) → W'
  53. Line(B_1, C_1) → f_2
  54. Mirror(D_1, f_2) → E_1
  55. Segment(D_1, E_1) → g_2
  56. Intersect(f_2, g_2) → F_1
  57. Rotate(D_1, (-α), F_1) → G_1
  58. Rotate(B_1, (-α), F_1) → H_1
  59. Rotate(E_1, (-α), F_1) → I_1
  60. Rotate(C_1, (-α), F_1) → J_1
  61. Polygon(G_1, H_1, I_1, J_1) → poly6', g_3, h_2, i_2, j_2
  62. Intersect(c', a') → H
  63. Intersect(c_1, a_1) → I

AI Drawing Prompt Reference

Draw a rectangle by first creating two intersecting line segments, then drawing perpendicular lines from each segment to form four vertices. Connect these vertices to complete the rectangle. Next, rotate the rectangle around one of its sides by a certain angle to create a new rectangle. Finally, rotate a point around the center of the rectangle to a new position and connect these points to form another rotated shape.
The prompt above was compiled from the original drawing commands and is for reference only.