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Rotations in the Cartesian Plane

Rotations in the Cartesian Plane
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2022-06-17 20:08
Coordinate GeometryTransformationGeometric Construction
This example demonstrates rotations of figures in the Cartesian plane. Key mathematical concepts include rotation transformations and coordinate geometry. Using commands like Polygon, Textfield, Rotate, Distance, Circle, Segment, and Angle, the construction of rotated figures is illustrated. Suitable for students at the middle school level and above learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Textfield(d) → InputBox1
  3. Textfield(e) → InputBox2
  4. Rotate(A, α, D) → A'
  5. Rotate(B, α, D) → B'
  6. Rotate(C, α, D) → C'
  7. Polygon(A', B', C') → t1', c', a', b'
  8. Distance(D, A') → DA'
  9. Distance(D, A) → f
  10. Circle(D, f) → g
  11. Distance(D, B') → DB'
  12. Distance(D, B) → h
  13. Distance(D, C) → DC
  14. Circle(D, h) → k
  15. Circle(D, i) → p
  16. Segment(D, A) → l
  17. Rotate(Distance[D, A], α) → m
  18. Rotate(Distance[D, A], α) → n
  19. Rotate(D, α, D) → D'
  20. Rotate(A, α, D) → A'_{1}
  21. Segment(D', A'_{1}) → l'
  22. Angle(l, l') → β
  23. Textfield(q) → InputBox3
  24. Textfield(r) → InputBox4
  25. Textfield(s) → InputBox5
  26. Textfield(t) → InputBox6
  27. Textfield(u) → InputBox7
  28. Textfield(v) → InputBox8

AI Drawing Prompt Reference

Draw a triangle ABC in the Cartesian plane and rotate it around point D to form a new triangle A'B'C'. Measure the distance DA' from D to A', and draw a circle centered at D with radius DA'. Similarly, measure the distances DB' and DC' from D to B' and C', and draw circles centered at D with radii DB' and DC'. Finally, draw the line segment DA from D to A, and measure the length of the rotated segment after rotating DA by angle α to find the rotation angle β.
The prompt above was compiled from the original drawing commands and is for reference only.