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Motion Symmetry: Preserving the Mass Centre

Motion Symmetry: Preserving the Mass Centre
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2017-12-05 18:21
AngleTrigonometryTransformationGeometric Construction
This GeoGebra example visually demonstrates the invariance of the mass center under motion symmetry. Using a combination of geometric construction commands—including Point, Segment, CircleArc, Intersect, Ray, OrthogonalLine, Angle, Line, and Polygon—the construction tracks how specific transformations preserve the mass center position. Core mathematical concepts include symmetry, center of mass, geometric transformations, and trigonometric relationships. The example is suitable for high school mathematics, physics, and geometry transformation units, supporting both conceptual understanding and dynamic exploration.

GeoGebra Commands & Parameters

  1. Point(yAxis) → R
  2. Point(yAxis) → A
  3. Segment(A, S) → i
  4. Point(xAxis) → C
  5. Point(yAxis) → B
  6. CircleArc(A, R, B) → c
  7. Intersect(c, i) → T,
  8. Ray(A, C) → b
  9. OrthogonalLine(C, b) → d
  10. CircleArc(A, C, T) → Arc
  11. Point(d) → K
  12. Angle(C, A, Rotate[C, alfa, A]) → α
  13. OrthogonalLine(T, yAxis) → j
  14. OrthogonalLine(T, xAxis) → l
  15. Intersect(j, yAxis) → U
  16. Intersect(l, xAxis) → V
  17. Segment(A, V) → cosinus
  18. Segment(A, U) → sinus
  19. Segment(U, T) → s
  20. Segment(V, T) → t
  21. Segment(C, S) → tangens
  22. Point(yAxis) → D
  23. Point(yAxis) → L
  24. Point(d) → M
  25. Segment(A, J) → m
  26. Intersect(c, m) → O,
  27. OrthogonalLine(O, yAxis) → n
  28. OrthogonalLine(O, xAxis) → p
  29. Intersect(p, xAxis) → P
  30. Intersect(n, yAxis) → Q
  31. Segment(C, J) → q
  32. Segment(A, Q) → r
  33. Segment(A, P) → b_1
  34. Angle(J, A, V) → β
  35. Segment(P, O) → e
  36. Segment(O, Q) → f
  37. Point(xAxis) → W
  38. CircleArc(A, O, C) → g
  39. Segment(T, S) → a
  40. Segment(J, O) → h
  41. Segment(V, Q) → k
  42. Line(C, k) → a_1
  43. Intersect(a_1, yAxis) → F
  44. Line(F, xAxis) → c_1
  45. Line(S, xAxis) → d_1
  46. Point(d_1) → G
  47. Line(G, yAxis) → e_1
  48. Intersect(e_1, c_1) → H
  49. Segment(G, H) → v_{ab}
  50. Segment(G, S) → g_1
  51. Segment(H, F) → h_1
  52. Segment(F, C) → i_1
  53. Polygon(A, B_1, N, U) → p_{ea}, a_2, b_2, E_{a}, u
  54. Polygon(C_1, Z, Q, A) → p_{eb}, c_2, E_{b}, q_1, a_3
  55. Polygon(C, S, D_1, D_2) → p_{ia}, c_3, E_{0a}, d_2, d_3
  56. Polygon(C, F_2, F_1, J) → p_{ib}, c_4, f_2, E_{0b}, j_1