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P6 Symmetry Ex1 (Vertical axis)

P6 Symmetry Ex1 (Vertical axis)
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2020-05-26 20:29
FunctionTrigonometryCoordinate GeometryTransformationGeometric Construction
In collections P6 6S1 Symmetry (English Version)
This example demonstrates how to draw and verify geometric symmetry with a vertical axis using GeoGebra. Core math concepts include symmetry, geometric transformations, and coordinate geometry. Key GeoGebra commands and objects used are Segment, Mirror, Sequence, and If. Suitable for middle school and above students to understand symmetry principles and practice geometric constructions.

GeoGebra Commands & Parameters

  1. Segment(Blue10a, Blue10b) → Blue10
  2. Segment(Blue9a, Blue9b) → Blue9
  3. IndexOf(SelectedElement[ListNumSeg], ListNumSeg) → NumSeg
  4. Segment(Blue8a, Blue8b) → Blue8
  5. Segment(Blue7a, Blue7b) → Blue7
  6. Segment(Blue6a, Blue6b) → Blue6
  7. Segment(Blue5a, Blue5b) → Blue5
  8. Segment(Blue4a, Blue4b) → Blue4
  9. Segment(Blue3a, Blue3b) → Blue3
  10. Segment(Blue2a, Blue2b) → Blue2
  11. Segment(Blue1a, Blue1b) → Blue1
  12. IndexOf(SelectedElement[ListSymA], ListSymA) → NumSymA
  13. Element({SymA1, SymA2, SymA3, SymA4}, NumSymA) → SymA
  14. Mirror(Blue10b, SymA) → Blue10b'
  15. Mirror(Blue10a, SymA) → Blue10a'
  16. Segment(Blue10a', Blue10b') → RefBlue10
  17. Mirror(Blue9b, SymA) → Blue9b'
  18. Mirror(Blue9a, SymA) → Blue9a'
  19. Segment(Blue9a', Blue9b') → RefBlue9
  20. Mirror(Blue8b, SymA) → Blue8b'
  21. Mirror(Blue8a, SymA) → Blue8a'
  22. Segment(Blue8a', Blue8b') → RefBlue8
  23. Mirror(Blue7b, SymA) → Blue7b'
  24. Mirror(Blue7a, SymA) → Blue7a'
  25. Segment(Blue7a', Blue7b') → RefBlue7
  26. Mirror(Blue6b, SymA) → Blue6b'
  27. Mirror(Blue6a, SymA) → Blue6a'
  28. Segment(Blue6a', Blue6b') → RefBlue6
  29. Mirror(Blue5b, SymA) → Blue5b'
  30. Mirror(Blue5a, SymA) → Blue5a'
  31. Segment(Blue5a', Blue5b') → RefBlue5
  32. Mirror(Blue4b, SymA) → Blue4b'
  33. Mirror(Blue4a, SymA) → Blue4a'
  34. Segment(Blue4a', Blue4b') → RefBlue4
  35. Mirror(Blue3b, SymA) → Blue3b'
  36. Mirror(Blue3a, SymA) → Blue3a'
  37. Segment(Blue3a', Blue3b') → RefBlue3
  38. Mirror(Blue2b, SymA) → Blue2b'
  39. Mirror(Blue2a, SymA) → Blue2a'
  40. Segment(Blue2a', Blue2b') → RefBlue2
  41. Mirror(Blue1b, SymA) → Blue1b'
  42. Mirror(Blue1a, SymA) → Blue1a'
  43. Segment(Blue1a', Blue1b') → RefBlue1
  44. Defined(IndexOf[RefBlue1, List1]) → Match1
  45. Sequence(Sequence[(s, t), s, -14, 12], t, -8, 8) → ListDots
  46. If(NumSeg ≟ 1, Match1, NumSeg ≟ 6, Match6, NumSeg ≟ 7, Match7, NumSeg ≟ 8, Match8, NumSeg ≟ 9, Match9, Match10, NumSeg ≟ 2, Match2, NumSeg ≟ 3, Match3, NumSeg ≟ 4, Match4, NumSeg ≟ 5, Match5) → Match

AI Drawing Prompt Reference

Draw a figure with vertical axis symmetry. Start by creating ten blue line segments at various positions and orientations, forming an irregular polyline pattern. Then define a vertical symmetry axis. For each blue segment, reflect its two endpoints across this axis to get mirrored points, and connect these points to form ten new red segments, which are the symmetric counterparts. Finally, add a grid of evenly spaced gray dots in the background as a reference, and verify that each red segment coincides with its corresponding blue segment to confirm symmetry. The overall result should show clear left-right mirror symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.