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Motion Control

Motion Control
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2015-03-11 11:32
VectorTransformationGeometric Construction
This example demonstrates how to recognize motions and the information needed for each using geometric transformations. It involves transformations, vectors, and point movements. Using GeoGebra commands such as Polygon, Translate, and Rotate, it dynamically shows the movement and transformation of points. Suitable for middle school and above students to learn about geometric transformations and motion control.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Line(E, F) → e
  3. Mirror(A, e) → A'
  4. Mirror(B, e) → B'
  5. Mirror(C, e) → C'
  6. Mirror(D, e) → D'
  7. Polygon(A', B', C', D') → Preimage, a', b', c', d'
  8. Vector(G, H) → u
  9. Translate(A', u) → A''
  10. Translate(B', u) → B''
  11. Translate(C', u) → C''
  12. Translate(D', u) → D''
  13. Polygon(A'', B'', C'', D'') → Target1, a'', b'', c'', d''
  14. Line(I, J) → f
  15. Mirror(A', f) → A''_1
  16. Mirror(B', f) → B''_1
  17. Mirror(C', f) → C''_1
  18. Mirror(D', f) → D''_1
  19. Polygon(A''_1, B''_1, C''_1, D''_1) → Target2, a''_1, b''_1, c''_1, d''_1
  20. Circle(K, 2) → g
  21. Point(g) → L
  22. Segment(K, L) → h
  23. Point(g) → M
  24. Segment(K, M) → i
  25. Angle(L, K, M) → α
  26. Rotate(A', α, K) → A''_2
  27. Rotate(B', α, K) → B''_2
  28. Rotate(C', α, K) → C''_2
  29. Rotate(D', α, K) → D''_2
  30. Polygon(A''_2, B''_2, C''_2, D''_2) → Target3, a''_2, b''_2, c''_2, d''_2
  31. Vector(N, O) → v
  32. Translate(A', v) → A''_3
  33. Translate(B', v) → B''_3
  34. Translate(C', v) → C''_3
  35. Translate(D', v) → D''_3
  36. Polygon(A''_3, B''_3, C''_3, D''_3) → poly1''_3, a''_3, b''_3, c''_3, d''_3
  37. Line(N, O) → j
  38. Mirror(A''_3, j) → P
  39. Mirror(B''_3, j) → Q
  40. Mirror(C''_3, j) → R
  41. Mirror(D''_3, j) → S
  42. Polygon(P, Q, R, S) → Target4, p, q, r, s
  43. Vector(T, U) → w
  44. Translate(A', w) → A''_4
  45. Translate(B', w) → B''_4
  46. Translate(C', w) → C''_4
  47. Translate(D', w) → D''_4
  48. Polygon(A''_4, B''_4, C''_4, D''_4) → Translated, a''_4, b''_4, c''_4, d''_4
  49. Circle(Center, 2) → t
  50. Point(t) → W
  51. Segment(Center, W) → l
  52. Point(t) → Z
  53. Segment(Center, Z) → m
  54. Angle(W, Center, Z) → Angle
  55. Rotate(A', Angle, Center) → A''_5
  56. Rotate(B', Angle, Center) → B''_5
  57. Rotate(C', Angle, Center) → C''_5
  58. Rotate(D', Angle, Center) → D''_5
  59. Polygon(A''_5, B''_5, C''_5, D''_5) → Rotation, a''_5, b''_5, c''_5, d''_5
  60. Line(V, A_1) → Line
  61. Mirror(A', Line) → A''_6
  62. Mirror(B', Line) → B''_6
  63. Mirror(C', Line) → C''_6
  64. Mirror(D', Line) → D''_6
  65. Polygon(A''_6, B''_6, C''_6, D''_6) → Reflection, a''_6, b''_6, c''_6, d''_6
  66. Vector(B_1, C_1) → z
  67. Translate(A', z) → A''_7
  68. Translate(B', z) → B''_7
  69. Translate(C', z) → C''_7
  70. Translate(D', z) → D''_7
  71. Polygon(A''_7, B''_7, C''_7, D''_7) → Preimage', a''_7, b''_7, c''_7, d''_7
  72. Line(B_1, C_1) → a_1
  73. Mirror(A''_7, a_1) → D_1
  74. Mirror(B''_7, a_1) → E_1
  75. Mirror(C''_7, a_1) → F_1
  76. Mirror(D''_7, a_1) → G_1
  77. Polygon(D_1, E_1, F_1, G_1) → GlideReflection, d_1, e_1, f_1, g_1