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Exploration of Basic Transformations by lisagebbie

Exploration of Basic Transformations by lisagebbie
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2014-09-25 05:25
VectorTransformationGeometric Construction
This example illustrates four basic geometric transformations: reflection, rotation, enlargement, and translation. Using GeoGebra commands such as Polygon, Dilate, Ray, Rotate, etc., you can visually understand these transformation concepts. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Polygon(C, D, B) → poly1, b, c, d
  2. Dilate(C, a, A) → C'_1
  3. Dilate(D, a, A) → D'_1
  4. Dilate(B, a, A) → B'_1
  5. Polygon(C'_1, D'_1, B'_1) → poly1'_1, b', c', d'
  6. Ray(A, C) → e
  7. Ray(A, B) → f
  8. Ray(A, D) → g
  9. Rotate(C, (-α), A) → C'_3
  10. Rotate(D, (-α), A) → D'_3
  11. Rotate(B, (-α), A) → B'_3
  12. Polygon(C'_3, D'_3, B'_3) → poly1'_3, b'_2, c'_2, d'_2
  13. Point(xAxis) → E
  14. Line(F, E) → h
  15. Mirror(C, h) → C'
  16. Mirror(D, h) → D'
  17. Mirror(B, h) → B'
  18. Polygon(C', D', B') → poly1', b'_3, c'_3, d'_3
  19. Vector(A, G) → z
  20. Angle(G, A, H) → β
  21. Vector(I, J) → u
  22. Translate(C, u) → C'_2
  23. Translate(D, u) → D'_2
  24. Translate(B, u) → B'_2
  25. Polygon(C'_2, D'_2, B'_2) → poly2, b'_1, c'_1, d'_1
  26. Vector(C, C'_2) → w
  27. Vector(B, B'_2) → v
  28. Vector(D, D'_2) → i

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, then perform dilation, rotation, and translation transformations. First, dilate quadrilateral ABCD with point A as the center to get quadrilateral A'B'C'D'. Next, rotate quadrilateral A'B'C'D' counterclockwise around point A to get quadrilateral A''B''C''D''. Then, mirror quadrilateral A''B''C''D'' across the x-axis to get quadrilateral A'''B'''C'''D'''. Finally, draw vectors from point A to points G and H to get vectors z and β, and then translate quadrilateral ABCD along vector z to get quadrilateral A''B''C''D''.
The prompt above was compiled from the original drawing commands and is for reference only.