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Point Rotation

Point Rotation
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2019-04-02 11:45
VectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the dynamic rotation of a point around a fixed center. It involves core concepts like rotation, circle, polygon, angle, and coordinate geometry. Construction highlights include DynamicCoordinates for point creation, Rotate for transformation, CircleArc for arc drawing, Polygon for shape formation, and If for conditional logic. Suitable for high school mathematics education to understand transformations and coordinate geometry applications.

GeoGebra Commands & Parameters

  1. DynamicCoordinates(P0, round(x(P0)), round(y(P0))) → P
  2. Point(yAxis) → O
  3. Rotate(P, 360° - δ, O) → R4'
  4. Rotate(P, 270° + δ, O) → R4
  5. CircleArc(O, R4, R4') → c4
  6. Rotate(P, 180° + δ, O) → R3
  7. Rotate(P, 90° + δ, O) → R2
  8. Rotate(P, 270° - δ, O) → R3'
  9. CircleArc(O, R3, R3') → c3
  10. Rotate(P, 180° - δ, O) → R2'
  11. CircleArc(O, R2, R2') → c2
  12. Rotate(P, δ, O) → R1
  13. Rotate(P, 90° - δ, O) → R1'
  14. CircleArc(O, R1, R1') → c1
  15. Point(xAxis) → B
  16. Point({P, c1, Rotate[P, 90°, O], c2, Rotate[P, 180°, O], c3, Rotate[P, 270°, O], c4}) → P'
  17. Angle(P, O, P') → α
  18. Rotate(Q, α, O) → Q'_2
  19. Polygon(O, Q'_2, P') → t1, p', o, q'
  20. Polygon(O, Q, P) → t2, p, o_1, q
  21. Angle(P, Q, O) → β
  22. Angle(P', Q'_2, O) → γ
  23. If(P' ≟ P, false, true) → rotated
  24. Angle(P, O, P') → ε
  25. CircleArc(O, P, P') → d
  26. CircleArc(O, P', P) → e
  27. Angle(P', O, P) → ζ
  28. Rotate(Q, ε, O) → Q'