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Probability of Parallelogram Vertices

Probability of Parallelogram Vertices
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2020-04-18 04:53
Coordinate GeometryProbability & StatisticsGeometric Construction
This example demonstrates the probability distribution of randomly selecting vertices for a parallelogram. It involves core math concepts like probability & statistics, geometric constructions, vectors, and coordinate geometry. Key GeoGebra commands used include Circle, RandomPointIn, Midpoint, Mirror, Polygon, If, CountIf, Point, Rotate, CircleSector, LineBisector, and Intersect. It is suitable for high school mathematics education, helping students understand the intersection of random events and geometric figures in probability problems.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. RandomPointIn(c) → C
  3. RandomPointIn(c) → D
  4. RandomPointIn(c) → E
  5. Midpoint(C, E) → F
  6. Mirror(D, F) → D'
  7. Polygon(C, D, E, D') → q1, c_1, d, e, d'
  8. Midpoint(C, D) → G
  9. Mirror(E, G) → E'
  10. Polygon(E', C, E, D) → q2, e', c_2, e_1, d_1
  11. Midpoint(D, E) → H
  12. Mirror(C, H) → C'
  13. Polygon(D, C', E, C) → q3, d_2, c', e_2, c_3
  14. If(IsInRegion[E', c], true, false) → a
  15. If(IsInRegion[D', c], true, false) → b
  16. If(IsInRegion[C', c], true, false) → f
  17. CountIf(x ≟ true, L) → w
  18. Circle(I, J) → g
  19. Point(g) → K
  20. Rotate(K, i°, I) → K'
  21. CircleSector(I, K, K') → h
  22. Rotate(K', j°, I) → K''
  23. CircleSector(I, K', K'') → p
  24. Rotate(K'', k°, I) → K'''
  25. CircleSector(I, K'', K''') → q
  26. CircleSector(I, K''', K) → r
  27. LineBisector(K', K'') → m
  28. Intersect(p, m, 1) → M
  29. LineBisector(K'', K''') → n
  30. Intersect(q, n, 1) → N
  31. LineBisector(K''', K) → s
  32. Intersect(r, s, 1) → O
  33. LineBisector(K', K) → t
  34. Intersect(h, t, 1) → P