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Transforming a Leaping Frog

Transforming a Leaping Frog
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2019-02-27 12:38
VectorCoordinate GeometryTransformation
This example demonstrates how to transform a leaping frog using rotations, reflections, and translations. Key mathematical concepts include geometric transformations such as rotation, reflection, and translation. The construction uses GeoGebra commands like Point, Vector, Translate, Rotate, etc. Suitable for middle school math education to help students understand the basic principles of geometric transformations.

GeoGebra Commands & Parameters

  1. Point(yAxis) → F
  2. Vector(F, G) → u
  3. Translate(stroke1, u) → stroke1'
  4. Translate(stroke9, u) → stroke9'
  5. Translate(stroke8, u) → stroke8'
  6. Translate(stroke7, u) → stroke7'
  7. Translate(stroke6, u) → stroke6'
  8. Translate(stroke5, u) → stroke5'
  9. Translate(stroke4, u) → stroke4'
  10. Translate(stroke3, u) → stroke3'
  11. Translate(stroke2, u) → stroke2'
  12. Translate(stroke10, u) → stroke10'
  13. Translate(C, u) → C'
  14. Translate(D, u) → D'
  15. Translate(E, u) → E'
  16. Rotate(stroke1', α, H) →
  17. Rotate(stroke9', α, H) →
  18. Rotate(stroke8', α, H) →
  19. Rotate(stroke7', α, H) →
  20. Rotate(stroke6', α, H) →
  21. Rotate(stroke5', α, H) →
  22. Rotate(stroke4', α, H) →
  23. Rotate(stroke3', α, H) →
  24. Rotate(stroke2', α, H) →
  25. Rotate(stroke10', α, H) →
  26. Rotate(C', α, H) → C''
  27. Rotate(D', α, H) → D''
  28. Rotate(E', α, H) → E''
  29. Rotate(stroke1'', (-β), I) → stroke1'''
  30. Rotate(stroke9'', (-β), I) → stroke9'''
  31. Rotate(stroke8'', (-β), I) → stroke8'''
  32. Rotate(stroke7'', (-β), I) → stroke7'''
  33. Rotate(stroke6'', (-β), I) → stroke6'''
  34. Rotate(stroke5'', (-β), I) → stroke5'''
  35. Rotate(stroke4'', (-β), I) → stroke4'''
  36. Rotate(stroke3'', (-β), I) → stroke3'''
  37. Rotate(stroke2'', (-β), I) → stroke2'''
  38. Rotate(stroke10'', (-β), I) → stroke10'''
  39. Rotate(C'', (-β), I) → C'''
  40. Rotate(D'', (-β), I) → D'''
  41. Rotate(E'', (-β), I) → E'''
  42. Line(J, K) → a
  43. Mirror(C, a) → C'_1
  44. Mirror(D, a) → D'_1
  45. Mirror(E, a) → E'_1
  46. Vector(L, M) → v
  47. Translate(stroke1'_1, v) → stroke11
  48. Translate(stroke9'_1, v) → stroke12
  49. Translate(stroke8'_1, v) → stroke13
  50. Translate(stroke7'_1, v) → stroke14
  51. Translate(stroke6'_1, v) → stroke15
  52. Translate(stroke5'_1, v) → stroke16
  53. Translate(stroke4'_1, v) → stroke17
  54. Translate(stroke3'_1, v) → stroke18
  55. Translate(stroke2'_1, v) → stroke19
  56. Translate(stroke10'_1, v) → stroke20
  57. Translate(C'_1, v) → N
  58. Translate(D'_1, v) → O
  59. Translate(E'_1, v) → P

AI Drawing Prompt Reference

Draw a leaping frog animation. Start by creating a point F on the Y-axis and a vector u from F to another point G. Then, translate lines stroke1 to stroke10 along vector u. Next, rotate these translated lines around point H by angle α. Then, rotate these rotated lines around point I by -β. Finally, create a line a, and mirror points C, D, and E to the other side of line a to get C'_1, D'_1, and E'_1. Create a vector v and translate C'_1 and D'_1 to get new lines stroke11 and stroke12.
The prompt above was compiled from the original drawing commands and is for reference only.