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Rotation in Coordinate Plane: Geometric Transformation Example

Rotation in Coordinate Plane: Geometric Transformation Example
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2022-12-12 21:14
Coordinate GeometryTransformationGeometric Construction
In collections Translations, Rotations, Reflections Exercises
This example demonstrates rotation transformations in the coordinate plane using GeoGebra. It explains how to rotate shapes around a specified point by a given angle. Key mathematical concepts include rotation matrices, coordinate transformations, and geometric transformations. Construction involves using Random to generate random points, If for conditional logic, Rotate command for rotation, and SelectedElement/SelectedIndex for interactive operations. Suitable for middle school students learning geometric transformations or high school students reviewing rotation in coordinate geometry.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

On a coordinate plane, create a rotation check illustration: randomly place two reference points near a common pivot point, then generate their rotated counterparts. Choose a rotation angle from values like 90°, 180°, 270°, and corresponding negative angles, and determine whether the direction is clockwise or counterclockwise. Rotate one reference point about the pivot by the chosen angle to obtain its image, and rotate the other reference point about the same pivot to obtain a second image. Display the rotated points and add small text feedback markers indicating whether the compared rotation results match.
The prompt above was compiled from the original drawing commands and is for reference only.