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Slope Discovery: Dynamic Construction of Non-Vertical Lines

Slope Discovery: Dynamic Construction of Non-Vertical Lines
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2019-07-15 23:47
VectorCoordinate GeometryGeometric Construction
This example demonstrates the dynamic construction of the equation of a non-vertical line using geometric tools. Key mathematical concepts include slope, vector transformations, and the geometric interpretation of linear equations. Construction involves GeoGebra commands such as Vector, Translate, Dilate, Polygon, Segment, Line, Midpoint, and Slope to build the figure. It is suitable for high school students learning linear equations and geometric transformations, or as a practical case for mathematical modeling.

GeoGebra Commands & Parameters

  1. Vector((0, 0), (1, 0)) → u
  2. Translate(A, u) → A'
  3. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], A') → A'_1
  4. Dilate(A'_1, If[1 < o ≤ 2, 2 - o, 0], B) → H
  5. Dilate((0, 0), If[-1 < o ≤ 0, (-o), 0], A) → D_1
  6. Translate(G, u) → G'
  7. Translate(B, u) → B'
  8. Translate(C, u) → C'
  9. Translate(D, u) → D'
  10. Polygon(A, A', B) → poly1, b, a_1, a'
  11. Polygon(B, B', C) → poly2, c, b_1, b'
  12. Polygon(C, C', D) → poly3, d, c_1, c'
  13. Polygon(D, D', E) → poly4, e, d_1, d'
  14. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], B') → B'_1
  15. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], C') → C'_1
  16. Dilate(D, If[0 < o ≤ 1, 1 - o, 0], D') → D'_1
  17. Segment(A, A'_1) → p
  18. Segment(B, B'_1) → q
  19. Segment(C, C'_1) → r
  20. Segment(D, D'_1) → s
  21. Dilate(A'_1, If[2 < o ≤ 3, 3 - o, 0], B'_1) → I
  22. Vector(A'_1, I) → v
  23. Translate(A'_1, v) → J
  24. Translate(H, v) → H'
  25. Dilate(B'_1, If[3 < o ≤ 4, 4 - o, 0], C'_1) → K
  26. Vector(B'_1, K) → w
  27. Translate(J, w) → J'
  28. Translate(H', w) → H''
  29. Dilate(C'_1, If[4 < o ≤ 5, 5 - o, 0], D'_1) → M
  30. Vector(C'_1, M) → u_1
  31. Translate(J', u_1) → J''
  32. Translate(H'', u_1) → H'''
  33. Translate(L, u) → L'
  34. Translate(F, u) → F'
  35. Line(A, B) → f_1
  36. IntegralBetween(f, g, 0, 1) → e_1
  37. Translate(O, u) → O'
  38. IntegralBetween(f, g_1, 1, 2) → h_1
  39. IntegralBetween(f, h, 2, 3) → i_1
  40. Dilate(O, If[0 < p_1 ≤ 1, 1 - p_1, 0], O') → O'_1
  41. Dilate(L, If[0 < p_1 ≤ 1, 1 - p_1, 0], L') → L'_1
  42. Dilate(G, If[0 < p_1 ≤ 1, 1 - p_1, 0], G') → G'_1
  43. Segment(G, G'_1) → k_1
  44. Segment(O, O'_1) → l_1
  45. Segment(L, L'_1) → m_1
  46. Dilate(G'_1, If[1 < p_1 ≤ 2, 2 - p_1, 0], O) → P
  47. Segment(G'_1, P) → q_1
  48. Midpoint(O'_1, L) → Q
  49. Midpoint(L'_1, F) → R
  50. Dilate(G'_1, If[2 < p_1 ≤ 3, 3 - p_1, 0], O'_1) → S
  51. Vector(G'_1, S) → v_1
  52. Translate(G'_1, v_1) → T
  53. Translate(P, v_1) → P'
  54. Segment(T, P') → j_1
  55. Dilate(G'_1, If[3 < p_1 ≤ 4, 4 - p_1, 0], Q) → U
  56. Vector(G'_1, U) → w_1
  57. Translate(G'_1, w_1) → V
  58. Translate(P, w_1) → P'_1
  59. Segment(V, P'_1) → n_1
  60. Segment(O'_1, L) → r_1
  61. Dilate(O'_1, If[4 < p_1 ≤ 5, 5 - p_1, 0], L'_1) → W
  62. Vector(O'_1, W) → s_1
  63. Translate(O'_1, s_1) → Z
  64. Translate(L, s_1) → L'_2
  65. Segment(Z, L'_2) → t_1
  66. Dilate(O'_1, If[5 < p_1 ≤ 6, 6 - p_1, 0], R) → A_1
  67. Vector(O'_1, A_1) → u_2
  68. Translate(O'_1, u_2) → B_1
  69. Translate(L, u_2) → L'_3
  70. Segment(B_1, L'_3) → f_2
  71. Segment(C_1, A) → g_2
  72. Slope(f_1) → a_2
  73. Textfield(m) → InputBox1
  74. Distance(C_1, A) → distanceC1A
  75. Distance(A'_1, H) → c_2
  76. Vector(E_1, D_1) → v_2
  77. Vector(A'_1, H) → t
  78. Distance(E_1, D_1) → distanceE1D1
  79. Vector(J, H') → w_2
  80. Vector(J', H'') → c_2
  81. Vector(J'', H''') → d_2
  82. Distance(J, C) → distanceJC
  83. Distance(J', D) → distanceJ'D
  84. Distance(J'', E) → distanceJ''E