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Reflection Over Parallel Lines by Jennifer Tate

Reflection Over Parallel Lines by Jennifer Tate
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2016-07-12 03:23
PolygonTransformationGeometric Construction
This GeoGebra example demonstrates the geometric transformation of reflecting a shape across two parallel lines, illustrating properties of reflection, distance preservation, and symmetry. Users can interact with the construction to observe how a polygon and its vertices map under successive reflections, and how the composition of two reflections over parallel lines results in a translation. The construction utilizes GeoGebra commands including Line, Mirror, Intersect, Segment, OrthogonalLine, and Point objects to create and manipulate reflected images. Suitable for middle to high school geometry units on transformations, symmetry, and congruence, it provides a dynamic way to explore reflection properties and composition of isometries.

GeoGebra Commands & Parameters

  1. Line(A, B) → R1
  2. Point(Circle[C, 5.548885023137532]) → D
  3. Polygon(C, D, E, F, G, H, I, J) → poly1, c, d, e, f, g, h, i, j
  4. Mirror(C, R1) → C'
  5. Mirror(D, R1) → D'
  6. Mirror(E, R1) → E'
  7. Mirror(F, R1) → F'
  8. Mirror(G, R1) → G'
  9. Mirror(H, R1) → H'
  10. Mirror(I, R1) → I'
  11. Mirror(J, R1) → J'
  12. Polygon(C', D', E', F', G', H', I', J') → poly1', c', d', e', f', g', h', i', j'
  13. Line(K, R1) → k
  14. Mirror(C', k) → C''
  15. Mirror(D', k) → D''
  16. Mirror(E', k) → E''
  17. Mirror(F', k) → F''
  18. Mirror(G', k) → G''
  19. Mirror(H', k) → H''
  20. Mirror(I', k) → I''
  21. Mirror(J', k) → J''
  22. Polygon(C'', D'', E'', F'', G'', H'', I'', J'') → poly1'', c'', d'', e'', f'', g'', h'', i'', j''
  23. Segment(C, C') → l
  24. Segment(D, D') → m
  25. Segment(C', C'') → n
  26. Segment(D', D'') → p
  27. Distance(C, C') → distanceCC'
  28. Segment(C, C'') → q
  29. Segment(D, D'') → r
  30. Point(k) → L
  31. Distance(R1, k) → o
  32. Distance(R1, k) → distance
  33. Distance(E, E') → distanceEE'
  34. Distance(E', E'') → distanceE'E''
  35. Distance(E, E'') → distanceEE''
  36. Distance(F, F') → distanceFF'
  37. Distance(F', F'') → distanceF'F''
  38. Distance(F, F'') → distanceFF''
  39. Distance(G, G') → distanceGG'
  40. Distance(G', G'') → distanceG'G''
  41. Distance(G, G'') → distanceGG''
  42. Distance(H, H') → distanceHH'
  43. Distance(H', H'') → distanceH'H''
  44. Distance(H, H'') → distanceHH''
  45. Distance(I, I') → distanceII'
  46. Distance(I, I'') → distanceII''
  47. Distance(I', I'') → distanceI'I''
  48. Distance(J, J') → distanceJJ'
  49. Distance(J, J'') → distanceJJ''
  50. Distance(J', J'') → distanceJ'J''
  51. Point(k) → M
  52. OrthogonalLine(M, R1) → f_1
  53. Intersect(R1, f_1) → N
  54. Intersect(R1, f_1) → O
  55. Segment(O, M) → g_1
  56. Segment(C, C') → h_1
  57. Segment(C, C'') → i_1