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GeoGebra Geometric Construction: Wolf's Locus

GeoGebra Geometric Construction: Wolf's Locus
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2023-02-22 07:55
FunctionGeometric ConstructionLocus
In collections Function Arts
This GeoGebra example demonstrates the trajectory of a wolf. Key mathematical concepts include geometric construction and locus. It uses points, functions, and locus objects and commands. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. (10.5, -4.41)
  2. (5.39, -3.56)
  3. (-15.06, 10.64)
  4. (15.11, -10.64)
  5. f(x) = If[-5 < x < 5, (0.18 * x^(2)) - 8]
  6. (x / 2)^(2) + ((y + 5.7) / 1)^(2) = 1
  7. g(x) = If[-2 < x < -1, (-2 * x) - 9.5]
  8. h(x) = If[1 < x < 2, (2 * x) - 9.5]
  9. p(x) = If[-1 < x < 1, (0.4 * abs(x)) - 8]
  10. q(x) = If[-7 < x < 7, (0.08 * x^(2)) - 9.5]
  11. r(x) = If[-9.2 < x < -7, abs(x + 8.1) - 6.8]
  12. s(x) = If[7 < x < 9.2, abs(x - 8.1) - 6.8]
  13. (x - 3.5)^(2) + (y + 0.9)^(2) = 0.15
  14. (x + 3.5)^(2) + (y + 0.9)^(2) = 0.15
  15. t(x) = If[-3.5 < x < -1, (x + 3.5)^(2) - 5.9]
  16. f_{1}(x) = If[1 < x < 3.5, (x - 3.5)^(2) - 5.9]
  17. g_{1}(x) = If[-3 < x < 3, (0.9 * abs(x)) + 0.9]
  18. h_{1}(x) = If[-2 < x < 2, (-0.5 * abs(x)) + 6.3]
  19. (0.05 * (y + 6)^(2)) = x + 9.3
  20. Numeric c_{1:}(1.0)
  21. c_{1:} - (0.05 * (y + 6)^(2)) = x - 9.3
  22. p_{1}(x) = If[3 < x < 6.9, (-0.7 * x) + 5.85]
  23. q_{1}(x) = If[-6.9 < x < -3, (0.7 * x) + 5.85]
  24. r_{1}(x) = If[2 < x < 4, (0.3 * x) - 1.5]
  25. s_{1}(x) = If[-4 < x < -2, (-0.3 * x) - 1.5]
  26. t_{1}(x) = If[2 < x < 4.1, (-0.2 * x) - 0.6]
  27. f_{2}(x) = If[-4.1 < x < -2, (0.2 * x) - 0.6]
  28. g_{2}(x) = If[4 < x < 4.18, (-7 * abs(x - 4)) - 0.2]
  29. h_{2}(x) = If[-4.18 < x < -4, (-7 * abs(x + 4)) - 0.2]
  30. p_{2}(x) = If[6.8 < x < 9.3, sqrt((-((x - 9.3) / 0.05))) - 5.7]
  31. q_{2}(x) = If[-9.3 < x < -6.8, sqrt((x + 9.3) / 0.05) - 5.7]
  32. r_{2}(x) = If[-8.9 < x < -6.7, (x + 6.5)^(2) + 1]
  33. s_{2}(x) = If[6.7 < x < 8.9, (x - 6.5)^(2) + 1]
  34. t_{2}(x) = If[2 < x < 8.2, (1.6 * sqrt(x - 2)) + 5.3]
  35. f_{3}(x) = If[-8.2 < x < -2, (1.6 * sqrt((-(x + 2)))) + 5.3]
  36. g_{3}(x) = If[8.1 < x < 8.92, (-3.8 * (x - 8.1)^(2)) + 9.25]
  37. h_{3}(x) = If[-8.9 < x < -8.1, (-3.8 * (x + 8.1)^(2)) + 9.25]
  38. p_{3}(x) = If[-7.2 < x < -4, (1.6 * sqrt((-(x + 4)))) + 5.2]
  39. q_{3}(x) = If[4 < x < 7.2, (1.6 * sqrt(x - 4)) + 5.2]
  40. r_{3}(x) = If[4 < x < 6.1, (-1.2 * sqrt(x - 4)) + 5.2]
  41. s_{3}(x) = If[-6.1 < x < -4, (-1.2 * sqrt((-(x + 4)))) + 5.2]
  42. t_{3}(x) = If[6 < x < 7.24, (3 * (x - 6)^(2)) + 3.45]
  43. f_{4}(x) = If[-7.24 < x < -6, (3 * (x + 6)^(2)) + 3.45]
  44. g_4(x) = If[6 < x < 7.24, (3 * (x - 6)^(2)) + 3.45]

AI Drawing Prompt Reference

Create a coordinate-plot illustration of a wolf’s path. Mark four specified points as key positions. Then draw several piecewise-defined locus curves that appear only within their stated x-intervals: segments formed from parabolas, straight lines, absolute-value lines, and square-root arcs. Use equation-style definitions for these curves so the shown parts match their corresponding domain restrictions. Also include two small circles/loops given by equations with centers at (-3.5, -0.9) and (3.5, -0.9) and radius about 0.15. Combine all pieces into one continuous looking trajectory.
The prompt above was compiled from the original drawing commands and is for reference only.