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Rotation in Coordinate Plane Example

Rotation in Coordinate Plane Example
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2022-12-12 21:10
Coordinate GeometryTransformationGeometric Construction
In collections Translations, Rotations, Reflections Exercises
This example demonstrates geometric rotation in the coordinate plane. Key mathematical concepts include rotation, coordinate transformation, and geometric transformations. Construction involves GeoGebra commands like Rotate, SelectedElement, and SelectedIndex. Suitable for middle or high school mathematics courses to understand geometric transformations and coordinate system applications.

GeoGebra Commands & Parameters

  1. Random(1, 4) → n
  2. Random(0, 1) → dir
  3. If(n ≟ 1, 90°, n ≟ 2, 180°, n ≟ 3, 270°, 360°) → α
  4. Random(-15, 15) → a
  5. Random(-15, 15) → b
  6. If(dir ≟ 0, α, (-α)) → β
  7. Random(-15, 15) → c
  8. Random(-15, 15) → d
  9. If(dir ≟ 0, "counterclockwise", "clockwise") → text2
  10. Rotate(B, β, A) → B'
  11. Rotate(A, β, B) → A'
  12. If(C ≟ A', "√", "X") → text8
  13. Textfield(C) → InputBox1
  14. Rotate(A, (-β), B) → A'_{1}
  15. If(C ≟ A'_{1}, "√", "X") → text9
  16. SelectedElement(l1) → text10
  17. SelectedElement(l1) → text11
  18. SelectedElement(l1) → text12
  19. SelectedElement(l1) → text13
  20. SelectedIndex(l1) → e
  21. SelectedIndex(l2) → f
  22. If(e ≟ 2 ∧ f ≟ 2, 90°, e ≟ 3 ∧ f ≟ 3, -180°, e ≟ 4 ∧ f ≟ 3, -270°, e ≟ 5 ∧ f ≟ 3, -360°, e ≟ 3 ∧ f ≟ 2, 180°, e ≟ 4 ∧ f ≟ 2, 270°, e ≟ 5 ∧ f ≟ 2, 360°, e ≟ 2 ∧ f ≟ 3, -90°) → g
  23. Rotate(B, g, A) → B'_{1}
  24. If(B' ≟ B'_{1}, "√", "X") → text16

AI Drawing Prompt Reference

Draw a geometric rotation example in the coordinate plane, showing a point rotating around another point by a randomly chosen angle (90°, 180°, 270°, or 360°), label the rotation direction (clockwise or counterclockwise), and compare if the rotated point coincides with the original, with text annotations explaining key relationships.
The prompt above was compiled from the original drawing commands and is for reference only.