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Translating and Rotating: Polygon Transformation Demo

Translating and Rotating: Polygon Transformation Demo
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2017-12-04 21:18
PolygonVectorTransformationGeometric ConstructionSlider Animation
This GeoGebra example dynamically demonstrates the transformation of a polygon (poly1) under translation (Translate) and rotation (Rotate), visually showing changes in position and orientation on the plane. Core mathematical concepts include planar geometry transformations, vectors, and composition of transformations. Construction highlights: uses Polygon to create the initial polygon, Intersect to find intersection points, Vector to define translation vectors, Rotate for rotation, Translate for translation, and generates transformed objects (e.g., poly1', g', h') and corresponding vertices (A', B', etc.). Suitable for middle and high school students learning geometric transformations, and for teachers to illustrate the geometric meaning and coordinate relationships in classroom demonstrations.

GeoGebra Commands & Parameters

  1. Polygon(G, H, A, B, C, D, E, F) → poly1, g, h, a, b_1, c, d_1, e, f
  2. Intersect(0, 2) → I
  3. Rotate(G, α, I) → G'_3
  4. Rotate(H, α, I) → H'_3
  5. Rotate(A, α, I) → A'_3
  6. Rotate(B, α, I) → B'_3
  7. Rotate(C, α, I) → C'_3
  8. Rotate(D, α, I) → D'_3
  9. Rotate(E, α, I) → E'_3
  10. Rotate(F, α, I) → F'_3
  11. Polygon(G'_3, H'_3, A'_3, B'_3, C'_3, D'_3, E'_3, F'_3) → poly1', g', h', a', b', c', d', e', f'
  12. Vector(K, L) → u
  13. Translate(G, u) → G'
  14. Translate(H, u) → H'
  15. Translate(A, u) → A'
  16. Translate(B, u) → B'
  17. Translate(C, u) → C'
  18. Translate(D, u) → D'
  19. Translate(E, u) → E'
  20. Translate(F, u) → F'
  21. Polygon(G', H', A', B', C', D', E', F') → poly1'_2, g'_2, h'_2, a'_2, b'_2, c'_2, d'_2, e'_2, f'_2
  22. Rotate(G', α, J) → G''
  23. Rotate(H', α, J) → H''
  24. Rotate(A', α, J) → A''
  25. Rotate(B', α, J) → B''
  26. Rotate(C', α, J) → C''
  27. Rotate(D', α, J) → D''
  28. Rotate(E', α, J) → E''
  29. Rotate(F', α, J) → F''
  30. Polygon(G'', H'', A'', B'', C'', D'', E'', F'') → poly2, g'', h'', a'', b'', c'', d'', e'', f''