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Reflections Over Parallel Lines

Reflections Over Parallel Lines
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2015-11-24 20:59
VectorTransformationGeometric Construction
This example demonstrates reflections over parallel lines. Key mathematical concepts include reflection and vector. Using GeoGebra commands such as Line, Mirror, Vector, and Translate, the construction of the reflected figure is shown. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(C, a) → b
  3. Polygon(D, E, F) → poly1, f, d, e
  4. Mirror(D, a) → D'
  5. Mirror(E, a) → E'
  6. Mirror(F, a) → F'
  7. Polygon(D', E', F') → poly1', f', d', e'
  8. Mirror(D', b) → D''
  9. Mirror(E', b) → E''
  10. Mirror(F', b) → F''
  11. Polygon(D'', E'', F'') → poly1'', f'', d'', e''
  12. Vector(G, H) → u
  13. Translate(D, u) → D'_1
  14. Translate(E, u) → E'_1
  15. Translate(F, u) → F'_1
  16. Polygon(D'_1, E'_1, F'_1) → poly1'_1, f'_1, d'_1, e'_1
  17. Vector(I, J) → v
  18. Point(b) → K
  19. Point(b) → L
  20. OrthogonalLine(L, a) → g
  21. Intersect(a, g) → M
  22. Distance(M, L) → distanceML
  23. Segment(M, L) → h
  24. Angle(B, M, L) → α
  25. Angle(M, L, K) → β
  26. Distance(I, J) → distanceIJ