MathPlotAI Logo MathPlotAI

P6 Symmetry Problem 1: Hanging Axis of Symmetry

P6 Symmetry Problem 1: Hanging Axis of Symmetry
Loading the math board and drawing, please wait…
2020-05-26 20:17
SequenceTransformationGeometric Construction
This GeoGebra example demonstrates the construction of symmetric figures about a vertical (hanging) axis of symmetry using mirror transformations. It visually shows how a set of blue line segments and points are reflected across the axis, illustrating the fundamental concept of axial symmetry. Core mathematical concepts include reflection, symmetry axis, corresponding points, and preservation of distances. The construction uses commands such as Segment to create line segments, Mirror for reflection, Sequence and If for conditional generation, IndexOf and Element for list manipulation, and defines multiple objects (Blue1 to Blue10 series, SymA1 to SymA4) to organize the symmetric structure. Suitable for upper primary or lower secondary students learning symmetry, and useful for classroom demonstrations or self-exploration of reflection properties.

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 vertical axis of symmetry. On one side, place several blue line segments, each defined by two endpoints. Reflect these blue segments across the axis to create corresponding reflected segments on the other side, keeping endpoints matched. Add a light dot grid in the background to help observe symmetry. The overall figure shows axial symmetry, emphasizing that corresponding points are equidistant from the axis and perpendicular to it, demonstrating that reflection preserves shape and distance.
The prompt above was compiled from the original drawing commands and is for reference only.