坐标系中的平行四边形：向量构造与几何验证

GeoGebra 命令及参数

1. Sequence(Sequence[(i, k), k, 0, 8], i, 0, 8) → PunkteFeld
2. Shuffle(Sequence[1, 7]) → HelperX, {2, 3, 5, 1, 4, 6, 7}
3. Join({{0}, HelperX}) → UrsprungXListe
4. Shuffle(Sequence[1, 7]) → HelperY, {5, 2, 4, 1, 7, 3, 6}
5. Join({{0}, HelperY}) → UrsprungYListe
6. Shuffle(Sequence[1, 7]) → AYList, {5, 2, 6, 1, 4, 7, 3}
7. Shuffle(Sequence[1, 7]) → AXList, {3, 5, 7, 2, 6, 4, 1}
8. Vector(Ursprung, A) → aCoords
9. Line(A, A + (-1, 0)) → i
10. Line(A, A + (0, 1)) → h
11. Max({distanceAnegX, distanceAposX, distanceAnegY, distanceAposY}) → maxf
12. Shuffle(Sequence[3, maxf - 1, 1]) → fList, {3, 4}
13. Random(1, fwert - 1) → erando
14. Circle(A, fwert) → c
15. Intersect(c, h) → CSucheNegY, CSuchePosY
16. Intersect(c, i) → CSuchePosX, CSucheNegX
17. Polygon(QE1, QE2, QE3, QE4) → coordsystem, qe1, qe2, qe3, qe4
18. RemoveUndefined({If[IsInRegion[CSuchePosY, coordsystem], y(CSuchePosY)], If[IsInRegion[CSuchePosX, coordsystem], y(CSuchePosX)], If[IsInRegion[CSucheNegX, coordsystem], y(CSucheNegX)], If[IsInRegion[CSucheNegY, coordsystem], y(CSucheNegY)]}) → CyOptionen
19. RemoveUndefined({If[IsInRegion[CSuchePosY, coordsystem], x(CSuchePosY)], If[IsInRegion[CSuchePosX, coordsystem], x(CSuchePosX)], If[IsInRegion[CSucheNegX, coordsystem], x(CSucheNegX)], If[IsInRegion[CSucheNegY, coordsystem], x(CSucheNegY)]}) → CxOptionen
20. Random(1, Length[CxOptionen]) → Crando
21. Vector(Ursprung, C) → cCoords
22. Segment(A, C) → j
23. OrthogonalLine(MittelpunktDeltoid, j) → k
24. Point(PunkteFeld) → InputPunkt
25. Min(AbstaendeMittelpunkt) → maxe
26. Shuffle(Sequence[1, maxe]) → eList, {1}
27. Circle(MittelpunktDeltoid, ewert) → d
28. Intersect(d, k) → D, B
29. Vector(Ursprung, DNew) → dCoords
30. Vector(Ursprung, B) → bCoords
31. Shuffle({2, 4}) → gesuchtList, {2, 4}
32. If(gesucht ≟ 1, x(aCoords), gesucht ≟ 2, x(bCoords), gesucht ≟ 3, x(cCoords), gesucht ≟ 4, x(dCoords)) → solx
33. If(gesucht ≟ 1, y(aCoords), gesucht ≟ 2, y(bCoords), gesucht ≟ 3, y(cCoords), gesucht ≟ 4, y(dCoords)) → soly
34. Circle(SolPunkt, 0.35) → ValidateCircle
35. IsInRegion(InputPunkt, ValidateCircle) → correctInputPunkt
36. Textfield(input1) → InputBox1
37. Textfield(input2) → InputBox2
38. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
39. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 5, 6, 3, 5, 8, 4, 9, 3, 10, 1, 0, 10, 10, 1, 6, 8, 2, 9, 2, 1, 5, 10, 8, 9, 4, 7, 6, 10, 2, 5, 7, 10, 5, 10, 6, 3, 10, 6, 4, 10, 8, 2, 0, 3, 3, 6, 6, 1, 10, 5, 10, 8, 1, 8, 0, 1, 9, 8, 10, 0, 7, 9, 8, 5, 7, 2, 8, 0, 4, 3, 0, 7, 6, 9, 3, 10, 7, 1, 3, 0, 9, 4, 8, 4, 4, 10, 8, 5, 8, 2, 7, 1, 5, 8, 10, 9, 3, 8, 6}
40. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
41. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 5, 4, 7, 2, 2, 9, 3, 8, 9, 8, 9, 2, 2, 4, 7, 3, 10, 6, 10, 10, 10, 5, 5, 4, 10, 4, 0, 2, 1, 8, 7, 3, 7, 8, 7, 10, 7, 0, 6, 5, 0, 10, 7, 7, 5, 0, 10, 8, 0, 5, 1, 3, 1, 9, 4, 3, 9, 5, 0, 0, 6, 0, 2, 8, 4, 5, 8, 6, 6, 8, 2, 5, 8, 2, 5, 1, 4, 2, 7, 2, 0, 8, 10, 5, 10, 10, 10, 4, 1, 1, 6, 1, 8, 2, 1, 2, 7, 5, 5}
42. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
43. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
44. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
45. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
46. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
47. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
48. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
49. Sequence(QE4 + (Vector[QE4, QE3] / 8 * i), i, 1, 7) → GrenzPunkteOben
50. Sequence(QE1 + (Vector[QE1, QE2] / 8 * i), i, 1, 7) → GrenzPunkteUnten
51. Sequence(QE1 + (Vector[QE1, QE4] / 8 * i), i, 1, 7) → GrenzPunkteLinks
52. Sequence(QE2 + (Vector[QE1, QE4] / 8 * i), i, 1, 7) → GrenzPunkteRechts
53. Sequence(Segment[GrenzPunkteOben(i), GrenzPunkteUnten(i)], i, 1, 9) → GitterVertikal
54. Sequence(Segment[GrenzPunkteRechts(i), GrenzPunkteLinks(i)], i, 1, 9) → GitterHorizontal
55. Line(Ursprung, HelpP1) → f
56. Line(Ursprung, HelpP2) → g
57. Intersect(g, QuadratKanten(2)) → EndXPos
58. Intersect(g, QuadratKanten(4)) → EndXNeg
59. Intersect(f, QuadratKanten(1)) → EndYNeg
60. Intersect(f, QuadratKanten(3)) → EndYPos
61. Segment(EndYPos, EndYNeg) → yAchsel
62. Segment(EndXPos, EndXNeg) → xAchsel
63. Polygon(C, B, A, DNew) → v1, l, m, n, p
64. Segment(C, B) → solb
65. Segment(B, A) → sola
66. Sequence(EndXNeg + (Vector[EndXNeg, EndXPos] * i / 8), i, 0, 8) → AchsenpunkteX
67. Sequence(EndYNeg + (Vector[EndYNeg, EndYPos] * i / 8), i, 0, 8) → AchsenpunkteY
68. Sequence(Distance[AchsenpunkteX(i), Ursprung], i, 1, 9) → BeschriftungXAchse
69. Sequence(Distance[AchsenpunkteY(i), Ursprung], i, 1, 9) → BeschriftungYAchse
70. Vector(Ursprung, InputPunkt) → OrangeCoords
71. Segment(A, DNew) → sold
72. Segment(DNew, C) → solc
73. Intersect(Line[A, C], Line[DNew, B]) → Center
74. Text(BeschA, E, false, true, 0, 0) → Text4
75. Angle(DNew, A, B) → α
76. Text(BeschB, F, false, true, 0, 0) → Text5
77. Text(BeschC, G, false, true, 0, 0) → Text6
78. Text(BeschD, H, false, true, 0, 0) → Text7
79. Circle(InputPunkt, 0.3) → e
80. Text(correctText, I, false, true, 0, 0) → Text13