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Drawing the Image After Rotation

Drawing the Image After Rotation
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2020-06-23 17:33
FunctionTransformationGeometric Construction
This example demonstrates how to draw images after a rotation. Key mathematical concepts include rotation transformation. Commands used include Random, Polygon, Segment, Rotate, Sequence, RandomElement, DynamicCoordinates, If, etc. Suitable for students at junior high school level and above learning geometric transformations.

GeoGebra Commands & Parameters

  1. Random(-3, 3) → i
  2. Random(-3, 3) → b
  3. Random(-3, 3) → c
  4. Random(-3, 3) → d
  5. Random(-3, 3) → e
  6. Random(-3, 3) → f
  7. Random(-2, 2) → g
  8. Random(-2, 2) → h
  9. Polygon(A, B, C) → t1, c_1, a_1, b_1
  10. Segment(A, B) → i_1
  11. Segment(B, C) → j
  12. Segment(C, A) → k
  13. Rotate(A, θ, O) → A'
  14. Rotate(B, θ, O) → B'
  15. Rotate(C, θ, O) → C'
  16. Polygon(A', B', C') → t1', c', a', b'
  17. Polygon(G, D, E, F) → q1, g_1, d_1, e_1, f_1
  18. Rotate(G, θ, O) → G'
  19. Rotate(D, θ, O) → D'
  20. Rotate(E, θ, O) → E'
  21. Rotate(F, θ, O) → F'
  22. Polygon(G', D', E', F') → q1', g', d', e', f'
  23. Sequence((90° * i), i, 1, 3, 1) → l1
  24. RandomElement(l1) → l
  25. Rotate(A, l, O) → A'_1
  26. Rotate(B, l, O) → B'_1
  27. Rotate(C, l, O) → C'_1
  28. Polygon(A'_1, B'_1, C'_1) → t1'_1, c'_1, a'_1, b'_1
  29. DynamicCoordinates(H, round(x(H)), round(y(H))) → A_1
  30. DynamicCoordinates(I, round(x(I)), round(y(I))) → B_1
  31. DynamicCoordinates(J, round(x(J)), round(y(J))) → C_1
  32. If(A_1 ≟ A'_1 ∧ B_1 ≟ B'_1 ∧ C_1 ≟ C'_1, "Correct!", "No. Try again.") → text1
  33. Polygon(A_1, B_1, C_1) → t2, n, p, q

AI Drawing Prompt Reference

Draw a triangle ABC, then rotate it around point O. Next, draw a rectangle GDEF and rotate it around point O. Then, randomly choose a rotation angle and rotate both the triangle ABC and the rectangle GDEF again. Observe the changes. Adjust the vertices of triangle ABC until they perfectly match the second rotation result of triangle A'B'C'.
The prompt above was compiled from the original drawing commands and is for reference only.