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Parabola Rotation Geometric Construction Example

Parabola Rotation Geometric Construction Example
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2018-07-01 20:31
FunctionCoordinate GeometryTransformationGeometric Construction
This example demonstrates the rotation of a parabola in a coordinate system, involving concepts such as rotational symmetry, function image transformation, and geometric construction techniques. Key construction steps include using GeoGebra's Rotate command, Point objects, function objects (f), and parameterized elements (a, b, c). Suitable for high school students learning analytic geometry and function transformations, or for mathematical teaching demonstrations and geometric construction practice.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Rotate(f, 45°, A) → f_1
  3. Rotate(f_1, 45°, A) → a
  4. Rotate(a, 45°, A) → a'
  5. Rotate(a', 45°, A) → a''
  6. Rotate(a'', 45°, A) → a'''
  7. Rotate(a''', 45°, A) → b
  8. Rotate(b, 45°, A) → b'
  9. Rotate(f, 45°, A) → f_2
  10. Rotate(f, 60°, A) → f_3
  11. Rotate(f_3, 60°, A) → c
  12. Rotate(a, 60°, A) → a'_1
  13. Rotate(a'_1, 60°, A) → d
  14. Rotate(d, 60°, A) → d'
  15. Rotate(d', 60°, A) → d''
  16. Rotate(a''', 60°, A) → e
  17. Rotate(f_3, 60°, A) → g
  18. Rotate(a, 60°, A) → a'_2
  19. Rotate(f_2, 60°, A) → h
  20. Rotate(d'', 60°, A) → d'''
  21. Rotate(d, 60°, A) → d'_1
  22. Rotate(d, 60°, A) → d'_2
  23. Rotate(a'', 60°, A) → a'''_1
  24. Rotate(f_3, β, A) → j
  25. Rotate(d''', β, A) → k
  26. Rotate(f_2, β, A) → l

AI Drawing Prompt Reference

Draw a parabola in a coordinate system and rotate it by 45 degrees. The rotated parabola maintains symmetry with the origin. Then, draw another parabola and rotate it by 60 degrees to create an angle relationship with the first parabola. The overall figure illustrates rotational symmetry and function transformation in geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.