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Exploring Reflections with Intersecting Lines

Exploring Reflections with Intersecting Lines
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2015-11-07 03:21
Coordinate GeometryGeometric Construction
In collections Glide Reflections Glide Reflections
This example demonstrates the process of geometric transformation using reflections and intersecting lines. It involves core mathematical concepts such as reflection transformation, geometric construction, and coordinate geometry. Key GeoGebra commands/objects used include Polygon, Line, Mirror, and Distance. Suitable for high school students learning geometric transformations, coordinate geometry, and foundational university mathematics.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F, G, H, I, J) → poly1, a, j, b, c, d, e, f, g, h, i
  2. Line(K, L) → Mirror1
  3. Mirror(A, Mirror1) → A'
  4. Mirror(B, Mirror1) → B'
  5. Mirror(C, Mirror1) → C'
  6. Mirror(D, Mirror1) → D'
  7. Mirror(E, Mirror1) → E'
  8. Mirror(F, Mirror1) → F'
  9. Mirror(G, Mirror1) → G'
  10. Mirror(H, Mirror1) → H'
  11. Mirror(I, Mirror1) → I'
  12. Mirror(J, Mirror1) → J'
  13. Polygon(A', B', C', D', E', F', G', H', I', J') → poly1'_1, a'_1, j'_1, b'_1, c'_1, d'_1, e'_1, f'_1, g'_1, h'_1, i'_1
  14. Mirror(A, Mirror1) → D16
  15. Mirror(B, Mirror1) → D17
  16. Mirror(C, Mirror1) → D18
  17. Mirror(D, Mirror1) → D19
  18. Mirror(E, Mirror1) → D20
  19. Mirror(F, Mirror1) → D21
  20. Mirror(G, Mirror1) → D22
  21. Mirror(H, Mirror1) → D23
  22. Mirror(I, Mirror1) → D24
  23. Mirror(J, Mirror1) → D25
  24. Distance(C, Mirror1) → l
  25. Distance(A, Mirror1) → B2
  26. Distance(B, Mirror1) → B3
  27. Distance(C, Mirror1) → B4
  28. Distance(D, Mirror1) → B5
  29. Distance(E, Mirror1) → B6
  30. Distance(F, Mirror1) → B7
  31. Distance(G, Mirror1) → B8
  32. Distance(H, Mirror1) → B9
  33. Distance(I, Mirror1) → B10
  34. Distance(J, Mirror1) → B11
  35. Distance(A', Mirror1) → D2
  36. Distance(B', Mirror1) → D3
  37. Distance(C', Mirror1) → D4
  38. Distance(D', Mirror1) → D5
  39. Distance(E', Mirror1) → D6
  40. Distance(F', Mirror1) → D7
  41. Distance(G', Mirror1) → D8
  42. Distance(H', Mirror1) → D9
  43. Distance(I', Mirror1) → D10
  44. Distance(J', Mirror1) → D11
  45. Line(M, K) → Mirror2
  46. Mirror(A', Mirror2) → A''
  47. Mirror(B', Mirror2) → B''
  48. Mirror(C', Mirror2) → C''
  49. Mirror(D', Mirror2) → D''
  50. Mirror(E', Mirror2) → E''
  51. Mirror(F', Mirror2) → F''
  52. Mirror(G', Mirror2) → G''
  53. Mirror(H', Mirror2) → H''
  54. Mirror(I', Mirror2) → I''
  55. Mirror(J', Mirror2) → J''
  56. Polygon(A'', B'', C'', D'', E'', F'', G'', H'', I'', J'') → poly2, a'', j'', b'', c'', d'', e'', f'', g'', h'', i''