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Double Reflection Transformation by himynameisfil

Double Reflection Transformation by himynameisfil
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2012-03-09 08:27
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the relationship between double reflection and rotation. Using GeoGebra commands such as Rotate, Mirror, and Polygon, you can observe the properties of reflection transformations. Key mathematical concepts include reflection transformation, rotation transformation, and geometric construction. This example is suitable for students at the junior high school level and above, focusing on geometric transformations.

GeoGebra Commands & Parameters

  1. Rotate(G, -β, F) → G'_1
  2. Line(F, G) → f
  3. Polygon(A, B, C, D, E, I) → poly1, a, b, c, d, e, i
  4. Mirror(A, f) → A'
  5. Mirror(B, f) → B'
  6. Mirror(C, f) → C'
  7. Mirror(D, f) → D'
  8. Mirror(E, f) → E'
  9. Mirror(I, f) → I'
  10. Polygon(A', B', C', D', E', I') → poly1', a', b', c', d', e', i'
  11. Line(F, G'_1) → g
  12. Mirror(A', g) → A''
  13. Mirror(B', g) → B''
  14. Mirror(C', g) → C''
  15. Mirror(D', g) → D''
  16. Mirror(E', g) → E''
  17. Mirror(I', g) → I''
  18. Polygon(A'', B'', C'', D'', E'', I'') → poly1'', a'', b'', c'', d'', e'', i''
  19. Circle(F, A) → k
  20. Circle(F, B) → p
  21. Circle(F, C) → q
  22. Circle(F, D) → r
  23. Circle(F, E) → s
  24. Circle(F, I) → t
  25. Rotate(G, -β, F) → G'
  26. Angle(G', F, G) → α
  27. Point(f) → H
  28. Angle(A'', F, A) → δ
  29. Segment(F, A) → n
  30. Segment(F, A'') → a_1