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Rotation Formula Demonstration

Rotation Formula Demonstration
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2015-11-11 10:05
TrigonometryCoordinate GeometryTransformationGeometric Construction
This example demonstrates the effect and formula application of rotation transformation in a 2D plane; core math concepts include rotation angle, trigonometric functions, coordinate transformation, and vector operations; construction highlights are derived from GeoGebra commands: Intersect, Segment, Point, Angle, OrthogonalLine, Rotate, CircleArc; suitable for high school and above mathematics learners to understand the geometric meaning and calculation methods of rotation transformation.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Segment(A, B) → d
  3. Point(xAxis) → C
  4. Angle(C, B, A) → α
  5. OrthogonalLine(A, xAxis) → e
  6. OrthogonalLine(A, yAxis) → f
  7. Point(e) → E
  8. Segment(A, E) → h
  9. Rotate(A, β°, B) → A'
  10. Segment(B, A') → i
  11. OrthogonalLine(A', yAxis) → j
  12. OrthogonalLine(A', xAxis) → k
  13. Angle(A, B, A') → β_1
  14. Intersect(yAxis, j) → D
  15. Intersect(k, xAxis) → G
  16. Segment(A', D) → c
  17. Segment(A', G) → g
  18. OrthogonalLine(A, yAxis) → l
  19. Intersect(yAxis, l) → H
  20. Segment(A, H) → n
  21. OrthogonalLine(A, xAxis) → m
  22. Intersect(m, xAxis) → F
  23. Segment(A, F) → p
  24. CircleArc(B, A, A') → q