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Alternate Interpretation of Slope

Alternate Interpretation of Slope
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2016-10-03 21:51
VectorFunctionCoordinate GeometryCalculus
In collections Slope
This example demonstrates the dynamic interpretation of the slope of a line and its geometric significance. It involves core mathematical concepts such as slope, vector, translation, dilation, integral, etc. Key construction elements include commands/objects like Vector, Translate, Polygon, Dilate, Segment, Line, IntegralBetween, Midpoint, Slope, Textfield, and Distance in GeoGebra. Suitable for high school coordinate geometry and calculus instruction to understand multiple representations of slope.

GeoGebra Commands & Parameters

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