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Translation Exploration by Maria Ahrens (2)

Translation Exploration by Maria Ahrens (2)
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2016-03-08 23:46
TriangleVectorCoordinate GeometryTransformationGeometric Construction
This example visually demonstrates the characteristics of triangle translation using sliders and involves core math concepts like vectors, geometric transformations, and coordinate geometry. It is constructed using commands such as Polygon, Vector, Translate, Rotate, and Mirror, making it suitable for high school students learning about geometric transformations, vectors, and coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → D, c, a, b
  2. Polygon(E, F, G) → H, g, e, f
  3. Vector(I, E) → u
  4. Polygon(J, K, L) → M, l, j, k
  5. Rotate(J, 90°, N) → J'
  6. Rotate(K, 90°, N) → K'
  7. Rotate(L, 90°, N) → L'
  8. Polygon(J', K', L') → M', l', j', k'
  9. Rotate(J, α, O) → J'_1
  10. Rotate(K, α, O) → K'_1
  11. Rotate(L, α, O) → L'_1
  12. Polygon(J'_1, K'_1, L'_1) → M'_1, l'_1, j'_1, k'_1
  13. Vector(P, Q) → v_1
  14. Translate(E, v_1) → E'_1
  15. Translate(F, v_1) → F'_1
  16. Translate(G, v_1) → G'_1
  17. Polygon(E'_1, F'_1, G'_1) → H'_1, g'_1, e'_1, f'_1
  18. Mirror(A, xAxis) → A'
  19. Mirror(B, xAxis) → B'
  20. Mirror(C, xAxis) → C'
  21. Polygon(A', B', C') → D', c', a', b'

AI Drawing Prompt Reference

Draw a triangle and its translation using a vector to demonstrate translation. Use a slider to control the translation vector, and show the effects of rotating the triangle by 90 degrees and an arbitrary angle. Finally, reflect the triangle across the x-axis to observe the transformation relationships.
The prompt above was compiled from the original drawing commands and is for reference only.