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Locus Introduction

Locus Introduction
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2016-05-17 06:04
CircleGeometric ConstructionLocus
This example demonstrates the construction and properties of various elementary locus types. It involves core mathematical concepts such as perpendicular bisectors, ellipses, circles, angles, and midpoints. The construction utilizes commands and objects like LineBisector, Point, Line, Segment, OrthogonalLine, Distance, Ellipse, Circle, Ray, Intersect, Angle, and Midpoint. It is suitable for middle school students and above, or as an educational aid for math competitions.

GeoGebra Commands & Parameters

  1. LineBisector(B_1, C_1) → a_1
  2. Point(a_1) → W
  3. LineBisector(B_1, C_1) → j
  4. Point(j) → Fixed
  5. Line(C_1, Fixed) → f_1
  6. Segment(Fixed, C_1) → k
  7. OrthogonalLine(W, k) → p
  8. Line(B_1, Fixed) → g_1
  9. Segment(Fixed, B_1) → l
  10. OrthogonalLine(W, l) → n
  11. LineBisector(B, C) → a
  12. Distance(F, G) → distanceFG
  13. Ellipse(K, L, M) → c
  14. Point(c) → N
  15. Segment(K, N) → d
  16. Segment(N, L) → e
  17. Circle(A, distanceFG) → f
  18. Point(f) → O
  19. Segment(A, O) → g
  20. Point(a) → P
  21. Segment(B, P) → h
  22. Segment(P, C) → i
  23. Distance(i, h) → b
  24. Segment(B_1, W) → h_1
  25. Segment(W, C_1) → i_1
  26. Distance(h_1, i_1) → b_1
  27. LineBisector(B_1, C_1) → m
  28. Ray(Fixed, B_1) → q
  29. Ray(Fixed, C_1) → r
  30. Intersect(n, g_1) → D
  31. Segment(W, D) → s
  32. Intersect(p, f_1) → E
  33. Segment(W, E) → t
  34. Segment(B_1, D) → c_1
  35. Segment(C_1, E) → d_1
  36. Angle(W, E, Fixed) → α
  37. Angle(Fixed, D, W) → β
  38. Midpoint(P, B) → I
  39. Midpoint(P, C) → J
  40. Midpoint(W, D) → Q
  41. Midpoint(W, E) → R
  42. Midpoint(A, O) → S

AI Drawing Prompt Reference

Draw a figure with perpendicular bisectors, ellipses, circles, and angles. Start by drawing perpendicular bisectors and finding their intersections, then draw segments, circles, and ellipses, construct perpendicular lines and angles, and finally mark midpoints.
The prompt above was compiled from the original drawing commands and is for reference only.