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Geometric Transformations Demo by Shane Canale

Geometric Transformations Demo by Shane Canale
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2014-10-13 22:10
VectorTransformationGeometric Construction
This example demonstrates various geometric transformations including similarity, translation, rotation, and reflection. It involves core math concepts like transformation, similarity, vectors, angles, and geometric construction. Key GeoGebra commands used are Polygon, Dilate, Ray, Translate, Vector, Rotate, Point, Line, Mirror, and Angle. Suitable for high school mathematics teaching or student exploration of transformation properties.

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. Translate(C, Vector[(horz, vert)]) → C'_3
  10. Translate(D, Vector[(horz, vert)]) → D'_3
  11. Translate(B, Vector[(horz, vert)]) → B'_4
  12. Polygon(C'_3, D'_3, B'_4) → poly1'_2, b'_1, c'_1, d'_1
  13. Vector(C, C'_3) → u
  14. Vector(B, B'_4) → v
  15. Vector(D, D'_3) → w
  16. Rotate(C, -α, A) → C'
  17. Rotate(D, -α, A) → D'
  18. Rotate(B, -α, A) → B'
  19. Polygon(C', D', B') → poly1'_3, b'_2, c'_2, d'_2
  20. Point(xAxis) → E
  21. Line(F, E) → h
  22. Mirror(C, h) → C'_2
  23. Mirror(D, h) → D'_2
  24. Mirror(B, h) → B'_2
  25. Polygon(C'_2, D'_2, B'_2) → poly1', b'_3, c'_3, d'_3
  26. Vector(A, G) → z
  27. Angle(G, A, H) → β
  28. Mirror(C'_2, xAxis) → I
  29. Mirror(D'_2, xAxis) → J
  30. Mirror(B'_2, xAxis) → B''

AI Drawing Prompt Reference

First, draw a triangle ABC. Then, scale triangle ABC to get A'B'C'. Next, translate the scaled triangle to get A''B''C''. After that, rotate triangle ABC by an angle to get A''B''C''. Finally, reflect the rotated triangle across a line to get A'''B'''C'''. The entire figure consists of these transformed triangles, illustrating basic geometric transformation concepts.
The prompt above was compiled from the original drawing commands and is for reference only.