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Translation #2

Translation #2
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2017-05-12 01:10
VectorTransformationGeometric Construction
This example demonstrates the concept of translation. Key mathematical concepts include translation vectors and geometric transformations. Using GeoGebra commands such as Polygon, Point, Vector, and Translate, a series of translated figures can be constructed. Suitable for students at the middle school level and above to learn about geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Point(a) → D
  3. Vector(A, D) → u
  4. Vector(C, B) → v
  5. Translate(A, u) → A'
  6. Translate(B, u) → B'
  7. Translate(C, u) → C'
  8. Polygon(A', B', C') → poly1', c', a', b'
  9. Translate(A', v) → A''
  10. Translate(B', v) → B''
  11. Translate(C', v) → C''
  12. Polygon(A'', B'', C'') → poly1'', c'', a'', b''
  13. Translate(A', u) → A''_1
  14. Translate(B', u) → B''_1
  15. Translate(C', u) → C''_1
  16. Polygon(A''_1, B''_1, C''_1) → poly1''_1, c''_1, a''_1, b''_1
  17. Polygon(D, A'', B') → poly2, b'_1, d, a''_2
  18. Vector(A'', D) → w
  19. Vector(B, B') → e
  20. Translate(D, w) → D'
  21. Translate(A'', w) → A'''
  22. Translate(B', w) → B''_2
  23. Polygon(D', A''', B''_2) → poly2', b''_2, d', a'''
  24. Translate(D, e) → D'_1
  25. Translate(A'', e) → A'''_1
  26. Translate(B', e) → B''_3
  27. Polygon(D'_1, A'''_1, B''_3) → poly2'_1, b''_3, d'_1, a'''_1

AI Drawing Prompt Reference

Draw a triangle ABC, then translate it twice: first with vector AD, then with vector CB. Next, translate triangle A'B'C' starting from point D along vector AD, and then translate it again with vector CB. Finally, translate triangle A''B''C'' starting from point D along vector AD, and then translate it again with vector CB.
The prompt above was compiled from the original drawing commands and is for reference only.