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Construction of a Perpendicular Bisector

Construction of a Perpendicular Bisector
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2015-01-23 21:58
CircleVectorCoordinate GeometryGeometric Construction
In collections Compass constructions
This example demonstrates how to construct the perpendicular bisector of a line segment using GeoGebra. Key math concepts include line segments, circles, intersection points, and symmetry. The construction involves commands like Circle, Vector, Translate, Intersect, Rotate, Segment, Line, and more, as outlined in the summary. Suitable for middle school and above, helping learners understand geometric constructions and symmetry principles.

GeoGebra Commands & Parameters

  1. Circle(A, C) → c
  2. Vector(A, B) → u
  3. Translate(c, u) → c'
  4. Intersect(c, c', 1) → D
  5. Intersect(c, c', 2) → E
  6. Rotate(D, a, A) → D'
  7. Rotate(D, (-a), A) → D'_1
  8. Rotate(D, a, B) → D'_2
  9. Rotate(D, (-a), B) → D'_3
  10. Rotate(E, a, A) → E'
  11. Rotate(E, (-a), A) → E'_1
  12. Rotate(E, a, B) → E'_2
  13. Rotate(E, (-a), B) → E'_3
  14. Segment(A, B) → b
  15. Segment(A, D') → d
  16. Segment(A, D'_1) → e
  17. Segment(B, D'_2) → f
  18. Segment(B, D'_3) → g
  19. Segment(B, E'_2) → h
  20. Segment(B, E'_3) → i
  21. Segment(A, E) → j
  22. Segment(A, E'_1) → k
  23. Segment(A, E') → l
  24. Segment(B, E) → m
  25. Segment(B, D) → n
  26. Segment(A, D) → p
  27. Line(D, E) → q
  28. Intersect(q, b) → F
  29. Segment(F, B) → r
  30. Segment(F, A) → s
  31. Angle(D, F, A) → α
  32. CircleArc(A, D'_1, D') → t
  33. CircleArc(B, D'_3, D'_2) → c_1
  34. CircleArc(A, E'_1, E') → d_1
  35. CircleArc(B, E'_3, E'_2) → e_1
  36. Polygon(D, A, E, B) → poly1, d_2, a_1, e_2, b_1

AI Drawing Prompt Reference

Draw a line segment and create a circle with its midpoint as the center. Translate the circle to get two intersecting circles, and connect the intersection points with the endpoints of the line segment rotated by specific angles to form a symmetric shape. Finally, draw the perpendicular bisector of the line segment.
The prompt above was compiled from the original drawing commands and is for reference only.