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Dynamic Coordinates with Linear Interpolation

Dynamic Coordinates with Linear Interpolation
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2016-09-22 21:54
VectorCoordinate GeometryCalculusGeometric Construction
This example demonstrates the geometric representation of dynamic coordinates and linear interpolation, constructing dynamic figures through elements like vectors, points, and lines; core mathematical concepts include vector operations, linear equations, and the positional relationship between points and lines; construction highlights are derived from the GeoGebra command summary, utilizing commands/objects such as Vector, If, Invert, Line, OrthogonalLine, Angle, and Point; suitable for high school and above mathematics learners to understand the application of linear interpolation in coordinate geometry.

GeoGebra Commands & Parameters

  1. Vector(A) → u
  2. If(x(A_2) - x(A) ≠ 0, Angle[A_3, A, A_2], 90°) → n
  3. Invert(matrix1) → matrix2
  4. Line(A_2, A) → a
  5. OrthogonalLine(A, a) → b
  6. Line(((1, 0) * matrix1) + u, ((1, 1) * matrix1) + u) → c
  7. Line(((0, 0) * matrix1) + u, ((0, 1) * matrix1) + u) → d
  8. Line(((1, 0) * matrix1) + u, ((1, 1) * matrix1) + u) → e
  9. Line(((2, 0) * matrix1) + u, ((2, 1) * matrix1) + u) → f
  10. Line(((3, 0) * matrix1) + u, ((3, 1) * matrix1) + u) → g
  11. Line(((4, 0) * matrix1) + u, ((4, 1) * matrix1) + u) → h
  12. Line(((5, 0) * matrix1) + u, ((5, 1) * matrix1) + u) → i
  13. Line(((6, 0) * matrix1) + u, ((6, 1) * matrix1) + u) → j
  14. Line(((7, 0) * matrix1) + u, ((7, 1) * matrix1) + u) → k
  15. Line(((8, 0) * matrix1) + u, ((8, 1) * matrix1) + u) → l
  16. Line(((9, 0) * matrix1) + u, ((9, 1) * matrix1) + u) → m
  17. Line(((0, 0) * matrix1) + u, ((0, 1) * matrix1) + u) → p
  18. Line(((-1, 0) * matrix1) + u, ((-1, 1) * matrix1) + u) → q
  19. Line(((-2, 0) * matrix1) + u, ((-2, 1) * matrix1) + u) → r
  20. Line(((-3, 0) * matrix1) + u, ((-3, 1) * matrix1) + u) → s
  21. Line(((-4, 0) * matrix1) + u, ((-4, 1) * matrix1) + u) → t
  22. Line(((-5, 0) * matrix1) + u, ((-5, 1) * matrix1) + u) → a_1
  23. Line(((-6, 0) * matrix1) + u, ((-6, 1) * matrix1) + u) → b_1
  24. Line(((-7, 0) * matrix1) + u, ((-7, 1) * matrix1) + u) → c_1
  25. Line(((-8, 0) * matrix1) + u, ((-8, 1) * matrix1) + u) → d_1
  26. Line(((-9, 0) * matrix1) + u, ((-9, 1) * matrix1) + u) → e_1
  27. Line(((0, 0) * matrix1) + u, ((1, 0) * matrix1) + u) → f_1
  28. Line(((0, 1) * matrix1) + u, ((1, 1) * matrix1) + u) → g_1
  29. Line(((0, 2) * matrix1) + u, ((1, 2) * matrix1) + u) → h_1
  30. Line(((0, 3) * matrix1) + u, ((1, 3) * matrix1) + u) → i_1
  31. Line(((0, 4) * matrix1) + u, ((1, 4) * matrix1) + u) → j_1
  32. Line(((0, 5) * matrix1) + u, ((1, 5) * matrix1) + u) → k_1
  33. Line(((0, 6) * matrix1) + u, ((1, 6) * matrix1) + u) → l_1
  34. Line(((0, 7) * matrix1) + u, ((1, 7) * matrix1) + u) → m_1
  35. Line(((0, 8) * matrix1) + u, ((1, 8) * matrix1) + u) → n_1
  36. Line(((0, 9) * matrix1) + u, ((1, 9) * matrix1) + u) → p_1
  37. Line(((0, 0) * matrix1) + u, ((1, 0) * matrix1) + u) → q_1
  38. Line(((0, -1) * matrix1) + u, ((1, -1) * matrix1) + u) → r_1
  39. Line(((0, -2) * matrix1) + u, ((1, -2) * matrix1) + u) → s_1
  40. Line(((0, -3) * matrix1) + u, ((1, -3) * matrix1) + u) → t_1
  41. Line(((0, -4) * matrix1) + u, ((1, -4) * matrix1) + u) → a_2
  42. Line(((0, -5) * matrix1) + u, ((1, -5) * matrix1) + u) → b_2
  43. Line(((0, -6) * matrix1) + u, ((1, -6) * matrix1) + u) → c_2
  44. Line(((0, -7) * matrix1) + u, ((1, -7) * matrix1) + u) → d_2
  45. Line(((0, -8) * matrix1) + u, ((1, -8) * matrix1) + u) → e_2
  46. Line(((0, -9) * matrix1) + u, ((1, -9) * matrix1) + u) → f_2
  47. Vector((x(A), 0)) → v
  48. Angle(v, u) → α
  49. Line(C, D) → g_2
  50. Line(C_1, D_1) → h_2
  51. Point(b) → E
  52. Point(a) → F