MathPlotAI Logo MathPlotAI

Vector Addition and Geometric Construction

Vector Addition and Geometric Construction
Loading the math board and drawing, please wait…
2015-02-16 06:33
VectorCoordinate GeometryGeometric Construction
This example demonstrates the geometric meaning of vector addition by constructing a triangle, circle, and line segments. Key mathematical concepts include vector addition, median line, centroid, and coordinate geometry. Construction involves GeoGebra commands such as Circle, Line, Intersect, Segment, and Rotate. Suitable for middle or high school mathematics to understand the connection between vectors and geometry.

GeoGebra Commands & Parameters

  1. Circle(Turn, 1) → BqbCirc
  2. Circle(Turn, 1.5) → BdaCirc
  3. Line(Turn, xAxis) → b
  4. Circle(Turn, 2) → BheadCirc
  5. Intersect(BheadCirc, b, 1) → D
  6. Intersect(BheadCirc, b, 2) → A
  7. Segment(D, A) → j
  8. Intersect(BdaCirc, j, 2) → BdaStart
  9. Rotate(BdaStart, Bda, Turn) → BdaPt
  10. Ray(Turn, BdaPt) → Bray
  11. Textfield(Ada) → AdaInput
  12. Textfield(Ahead) → AheadInput
  13. If(0° < Ahead < 180°, "E", "W") → Aew
  14. If(90° < Ahead < 270°, "S", "N") → Ans
  15. If(0° ≤ Ahead ≤ 90°, Ahead, If[90° < Ahead ≤ 180°, 180° - Ahead, If[180° < Ahead ≤ 270°, Ahead - 180°, 360° - Ahead]]) → Aqb
  16. Point(yAxis) → AheadStart
  17. Point(xAxis) → AdaStart
  18. Intersect(xAxis, yAxis) → C
  19. Ray(C, AdaStart) → c
  20. Ray(C, AheadStart) → d
  21. Rotate(AdaStart, Ada, C) → AdaPt
  22. Circle(C, AdaStart) → AdaCirc
  23. Arc(AdaCirc, AdaStart, AdaPt) → AdaArc
  24. Rotate(C, Ada) → C'
  25. Ray(C', AdaPt) → Aray
  26. Circle(C, AheadStart) → AheadCirc
  27. Rotate(AheadStart, (-Ahead), C) → AheadPt
  28. Circle(C, 1.5) → AqbCirc
  29. Intersect(AqbCirc, d, 1) → AqbNorth
  30. Intersect(AqbCirc, yAxis, 1) → AqbSouth
  31. Intersect(AqbCirc, Aray, 1) → AqbPoint
  32. If(Ans ≟ "N", If[Aew ≟ "W", Arc[AqbCirc, AqbNorth, AqbPoint], Arc[AqbCirc, AqbPoint, AqbNorth]], If[Aew ≟ "W", Arc[AqbCirc, AqbPoint, AqbSouth], Arc[AqbCirc, AqbSouth, AqbPoint]]) → AqbArc
  33. Rotate(AheadStart, -0.01*°, C) → AheadDir
  34. Angle(AheadStart, C, AheadDir) → Hangle
  35. CircumcircleArc(AheadStart, AheadDir, AheadPt) → AheadArc
  36. Vector(C, Apoint) → Avec
  37. If(0° ≤ Bhead ≤ 90°, Bhead, If[90° < Bhead ≤ 180°, 180° - Bhead, If[180° < Bhead ≤ 270°, Bhead - 180°, 360° - Bhead]]) → Bqb
  38. Textfield(Amag) → AmagInput
  39. Textfield(Bmag) → BmagInput
  40. Textfield(Bda) → BdaInput
  41. Textfield(Bhead) → BheadInput
  42. Text(If[0° < Bhead < 180°, "E", "W"]) → Bew
  43. Text(If[90° < Bhead < 270°, "S", "N"]) → Bns
  44. Vector((Ax, Ay), (Ax + Bx, Ay + By)) → Bvec
  45. Vector(C, (Rx, Ry)) → Rvec
  46. Line(Turn, yAxis) → i
  47. Intersect(BheadCirc, i, 2) → BheadStart
  48. Intersect(BheadCirc, i, 1) → E
  49. Segment(BheadStart, E) → k
  50. Rotate(BheadStart, -0.01*°, Turn) → BheadDir
  51. Rotate(BheadStart, (-Bhead), Turn) → BheadPt
  52. CircumcircleArc(BheadStart, BheadDir, BheadPt) → BheadArc
  53. Arc(BdaCirc, BdaStart, BdaPt) → BdaArc
  54. Intersect(BqbCirc, k, 1) → BqbNorth
  55. Intersect(BqbCirc, Bray) → BqbPoint,
  56. Intersect(BqbCirc, k, 2) → BqbSouth
  57. If(Bns ≟ "N", If[Bew ≟ "W", Arc[BqbCirc, BqbNorth, BqbPoint], Arc[BqbCirc, BqbPoint, BqbNorth]], If[Bew ≟ "W", Arc[BqbCirc, BqbPoint, BqbSouth], Arc[BqbCirc, BqbSouth, BqbPoint]]) → BqbArc
  58. Angle(AdaStart, C, (Rx, Ry)) → Rda
  59. Angle((Rx, Ry), C, AheadStart) → Rhead
  60. If(90° < Rhead < 270°, "S", "N") → Rns
  61. If(0° < Rhead < 180°, "E", "W") → Rew
  62. If(0° ≤ Rhead ≤ 90°, Rhead, If[90° < Rhead ≤ 180°, 180° - Rhead, If[180° < Rhead ≤ 270°, Rhead - 180°, 360° - Rhead]]) → Rqb
  63. Ray((0, 0), (Rx, Ry)) → RRay
  64. Intersect(AheadCirc, RRay) → RheadPt,
  65. CircumcircleArc(AheadStart, AheadDir, RheadPt) → RheadArc
  66. Rotate(AdaStart, Rda, C) → RdaPt
  67. Arc(AdaCirc, AdaStart, RdaPt) → RdaArc
  68. Intersect(AqbCirc, RRay, 1) → RqbPoint
  69. If(Rns ≟ "N", If[Rew ≟ "W", Arc[AqbCirc, AqbNorth, RqbPoint], Arc[AqbCirc, RqbPoint, AqbNorth]], If[Rew ≟ "W", Arc[AqbCirc, RqbPoint, AqbSouth], Arc[AqbCirc, AqbSouth, RqbPoint]]) → RqbArc

AI Drawing Prompt Reference

The figure consists of a triangle, two circles, and several line segments, illustrating vector addition, medians, centroid, and coordinate geometry. The triangle's vertices intersect with circles to form line segments, which intersect circles to create rays after rotation. Arcs are drawn between circle centers and intersection points. Medians, centroid points, and points on the coordinate axes are included, with vector addition visualized through these geometric relationships. The layout reflects a logical construction sequence, suitable for understanding the connection between vectors and geometry.
The prompt above was compiled from the original drawing commands and is for reference only.