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Matrix Representation for a Counter-Clockwise Rotation by θ Degrees about (0, 0)

Matrix Representation for a Counter-Clockwise Rotation by θ Degrees about (0, 0)
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2020-07-14 03:29
TrigonometryMatrix
This example demonstrates the matrix representation for a counter-clockwise rotation by θ degrees about the origin. Key mathematical concepts include trigonometry and matrices. Using GeoGebra commands like Rotate, Angle, and SurdText, the construction of rotated points and figures is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → I
  3. Point(yAxis) → J
  4. Polygon(O, I, P, J) → q1, a, b, c, d
  5. Rotate(O, θ, O) → O'
  6. Rotate(I, θ, O) → I'
  7. Rotate(P, θ, O) → P'
  8. Rotate(J, θ, O) → J'
  9. Polygon(O', I', P', J') → q1', o', i', p', j'
  10. Angle(I, O, I') → α
  11. SurdText(I') → text1
  12. Angle(J, O, J') → β
  13. SurdText(J') → text2
  14. Segment(A, I') → f
  15. Segment(J', B) → g
  16. Angle(I', A, O) → γ
  17. Angle(J', B, O) → δ
  18. SurdText(x(I')) → text6
  19. SurdText(x(J')) → text7
  20. SurdText(y(I')) → text8
  21. SurdText(y(J')) → text9