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Shortest Distance from a Point to a Line Segment (Angle Bisector)

Shortest Distance from a Point to a Line Segment (Angle Bisector)
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2019-08-20 13:12
AngleCoordinate GeometryGeometric Construction
This example demonstrates the concept of the shortest distance from a point to a line segment using the angle bisector. Key mathematical concepts include distance, angle bisector, and perpendicular lines. Commands used include Segment, AngularBisector, Point, Angle, OrthogonalLine, Intersect, Distance. Suitable for middle school and above students to learn geometric construction and distance concepts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. AngularBisector(f, g) → h, i
  4. Point(i) → R
  5. Point(f) → P
  6. Segment(R, P) → j
  7. Angle(B, P, R) → α
  8. OrthogonalLine(R, f) → k
  9. Intersect(k, f) → F
  10. Distance(R, P) → distanceDE
  11. Point(g) → Q
  12. Ray(B, R) → l
  13. Segment(Q, R) → m
  14. Mirror(P, l) → P'
  15. Angle(R, Q, B) → β
  16. Circle(B, 4) → c
  17. Point(c) → D
  18. Point(c) → E
  19. CircleArc(B, D, E) → d
  20. Point(c) → G
  21. Point(c) → H
  22. CircleArc(B, G, H) → e
  23. Intersect(e, f) → I,
  24. Intersect(d, g) → J,
  25. Circle(I, 6) → p
  26. Circle(J, 6) → q
  27. Point(q) → K
  28. Point(q) → L
  29. CircleArc(J, K, L) → r
  30. Point(p) → M
  31. Point(p) → N
  32. CircleArc(I, M, N) → s
  33. Intersect(r, s) → O, , ,

AI Drawing Prompt Reference

Draw a line segment and its angle bisector. Take a point on the line segment, draw a perpendicular line from the point to the angle bisector, and connect the foot of the perpendicular to the endpoint of the line segment. Then, take another point on the line segment, connect it to the foot of the perpendicular, and measure the length. Next, draw circles centered at the endpoints of the line segment, intersecting them at two points. Connect these points and draw an arc. Finally, draw circles centered at the foot of the perpendicular and the intersection points of the arc, intersecting them at two points. Connect these points and draw another arc. The intersection of the two arcs is the desired point.
The prompt above was compiled from the original drawing commands and is for reference only.