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Girl in the Mirror

Girl in the Mirror
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2018-12-04 17:56
FunctionTransformationGeometric Construction
This example demonstrates a girl in the mirror. The core mathematical concepts involved are geometric transformations, specifically mirror transformations. Using GeoGebra commands such as Point, Intersect, Segment, OrthogonalLine, Line, Mirror, etc., the image of the girl in the mirror is constructed. Suitable for middle or high school geometry education to help students understand the concept of mirror transformations.

GeoGebra Commands & Parameters

  1. Point(yAxis) → F
  2. Intersect(xAxis, yAxis) → B_2
  3. Segment(B_2, F) → b
  4. Intersect(b, g) → A
  5. OrthogonalLine(L, b) → i
  6. Intersect(b, i) → B
  7. OrthogonalLine(C, b) → e
  8. Point(e) → I
  9. Point(e) → J
  10. Segment(J, I) → h
  11. Point(h) → H
  12. Intersect(c, i) → M
  13. Line(B_1, B_2) → d
  14. OrthogonalLine(B_1, d) → f
  15. Mirror(pic1, b) → pic2
  16. Mirror(H, b) → D
  17. OrthogonalLine(E, b) → a
  18. Intersect(a, c) → G
  19. Intersect(g, c) → K
  20. Mirror(M, b) → N
  21. Mirror(K, b) → O
  22. Segment(G, O) → j
  23. Segment(G, N) → k
  24. Intersect(b, j) → A'
  25. Intersect(b, k) → B'
  26. Angle(B', G, A') → α
  27. Segment(A', B') → l
  28. Segment(G, B') → p
  29. Segment(B', M) → q
  30. OrthogonalLine(B', b) → r
  31. Point(r) → P
  32. Angle(M, B', B) → β
  33. Angle(A', B', G) → γ
  34. Intersect(j, b) → Q
  35. Segment(G, Q) → a1
  36. Segment(K, Q) → b1
  37. OrthogonalLine(G, b) → c1
  38. Intersect(g, j) → R
  39. OrthogonalLine(R, c1) → d1
  40. Point(b) → U
  41. Intersect(b, d) → V
  42. Polygon(U, S, T, V) → poly1, u_1, s_1, t_1, v_1