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Locus of a Moving Point and a Line Segment

Locus of a Moving Point and a Line Segment
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2013-04-02 17:57
FunctionCoordinate GeometryLocus
This example demonstrates the locus of a moving point and a line segment. Key mathematical concepts include locus, line segment, distance, and circle. Using GeoGebra commands such as Segment, OrthogonalLine, Distance, and Circle, the construction of the locus of a moving point and a line segment is illustrated. Suitable for high school mathematics education, particularly in coordinate geometry and locus problems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Distance((1, 0), (2, 0)) → e
  4. OrthogonalLine(C, a) → r
  5. Circle(C, d) → q
  6. Intersect(q, r) → P', P
  7. Circle(A, d) → g
  8. OrthogonalLine(A, a) → i
  9. Intersect(g, i) → E, F
  10. Circle(B, d) → k
  11. OrthogonalLine(B, a) → l
  12. Intersect(k, l) → H, I
  13. Segment(F, I) → m
  14. Semicircle(I, H) → p
  15. Segment(H, P') → n
  16. Segment(F, P) → j
  17. Semicircle(E, F) → s
  18. Distance(P', a) → distanceP'a
  19. Distance(P', a) → h
  20. Distance(P, a) → distancePa

AI Drawing Prompt Reference

Draw the locus of a moving point and a line segment. Start by drawing line segment AB, then draw the perpendicular line b to AB. Calculate the distance between points (1,0) and (2,0) and use it as the radius to draw circle q. Use the intersection points P' and P of circle q and perpendicular line b to draw circle g and circle k, and then draw line segments m, semicircle p, line segments n and j, and line segments i and l. Finally, calculate the distances from P' and P to line segment AB to get distances h and distancePa.
The prompt above was compiled from the original drawing commands and is for reference only.