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在直线上找出点的乘法规则

在直线上找出点的乘法规则
几何画板及绘图内容加载中，请稍等……
2023-08-10 10:31
函数数列解析几何
本范例通过图形展示如何找出直线上点的乘法规则。核心数学概念涉及解析几何中的线性函数。使用了GeoGebra命令如Line、Sequence、KeepIf等。适合初中6-8年级学生学习。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.9741629072957583, 0.6902072668277874, 0.23054968573266038, 0.5102020742823086, 0.883139632801929, 0.1402842818648548, 0.8714365397368462, 0.5901526459051111, 0.29552178424947023, 0.5922931567833662, 0.8009021080123994, 0.7431908311243693, 0.3583733292382644, 0.9356976934232953, 0.4722340030961881, 0.8437985677346206, 0.049863519871137435, 0.34695596410497714, 0.7263337102636614, 0.938068388955514, 0.8301262757105818, 0.4428470708471403, 0.33579429941540284, 0.5437054639364494, 0.30449271275687095, 0.6987558414106785, 0.2915146766029237, 0.29050599124465876, 0.11645306504633175, 0.08472738189549063, 0.8963501171904368, 0.7116973174769031, 0.32753686574512036, 0.559672242723223, 0.8299753886224224, 0.3876876796183339, 0.46832308605891204, 0.8063585252934755, 0.16100321598496986, 0.7146225009463681, 0.039000089930957126, 0.09677074057694775, 0.5164525505893791, 0.5906814764005721, 0.3692919368242896, 0.47904608257658554, 0.12490217176687635, 0.3832753792825888, 0.9661519130059681, 0.5635169251862716, 0.21809208868412078, 0.9702136069130546, 0.3433948659786244, 0.21639463137853354, 0.03635130199978949, 0.22751310597675126, 0.38039990746720354, 0.2753227921560401, 0.026032341588531, 0.6258061099291707, 0.23716063487706524, 0.8114089842304535, 0.32212399460223096, 0.0762793939585577, 0.2602945186272195, 0.23741222382611168, 0.006390856894206577, 0.2557391472534008, 0.3391444626806203, 0.45151998931214876, 0.6407538898570474, 0.6787456445902936, 0.5028145203017438, 0.5105907715764072, 0.14717846553932745, 0.2727988845209838, 0.13787814479220822, 0.16587019083852778, 0.5290775008112806, 0.1802807217690613, 0.502581544491679, 0.3280062925522929, 0.6651637053331475, 0.8582717304879727, 0.6466360583413142, 0.9366957126071715, 0.4648015958559423, 0.4044599242169019, 0.7961522235770914, 0.37348603906848155, 0.12421145017898111, 0.6941460503171069, 0.6309154475574255, 0.4141400090656864, 0.4253687003675006, 0.49982462735984995, 0.6760360889208348, 0.9295361566892661, 0.9441188234306701, 0.2709821180013788, 0.09202928229540558, 0.39133572203151323, 0.20089438777606472, 0.30760294872162275, 0.7965880520663752, 0.7405897572010282, 0.44647209709583546, 0.0764115045675473, 0.8477102522027036, 0.8040903390553734, 0.026449591548804153, 0.4141028270961646, 0.24142357554708851, 0.6945891610471686, 0.2815478102184669, 0.056726482799606424, 0.2381243889455761, 0.817011574389803, 0.346461438803868, 0.9489882161002667, 0.53950524885048, 0.8334885565782305, 0.00778165325658615, 0.06152072626128351, 0.9631925028044034, 0.08540876601601548, 0.7615060804538081, 0.4481494356949645, 0.6545488691785178, 0.24076281083277923, 0.2428286689587528, 0.23884197924654652, 0.9046182284743457, 0.4598056564849364, 0.4352669817134002, 0.30737846341375635, 0.8798978679408045, 0.6915085243042377, 0.462737866614585, 0.5958179533089735, 0.2935208295010449, 0.7274010059232171, 0.5069318454517979, 0.800560393288217, 0.15851420475000222, 0.3482230865374709, 0.5332650140892339, 0.17721583933204435, 0.47207128327285247, 0.0023127663877402283, 0.3918021116687749, 0.623591704063627, 0.30523420842856896, 0.6628478323863889, 0.4548470216882004, 0.5218970817231724, 0.42503012792265266, 0.8739416537052126, 0.8903879326602254, 0.29273638029332144, 0.16593812851473178, 0.3931611221610349, 0.9702609815353266, 0.48462776681316183, 0.4745855266760899, 0.7002902959209224, 0.5437624712637046, 0.07363091883634534, 0.6157812055539448, 0.3891074971279551, 0.011491918228858899, 0.44820580735119836, 0.009389846597399254, 0.27057363959568664, 0.6304486209031969, 0.19464902093664863, 0.9561354293478742, 0.48214840166894807, 0.009832115304394845, 0.5383659316477135, 0.1261933621672192, 0.8989567266903894, 0.7876119579435221, 0.4558369802801838, 0.18738978607108167, 0.7482209849896537, 0.7507357413462451, 0.4714231798103679, 0.5299733585153615, 0.8587558256962066, 0.15683297344104408, 0.5521306778492635, 0.05225792001698014, 0.852390377794113, 0.22245225249023062, 0.0021162032924146056, 0.08595729637544083, 0.3339385650572041, 0.39223231366426553, 0.6970651570901637}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Sequence((n, questionLine(n)), n, -11, 11) → PointsLine
  4. Polygon({DataMin, (x(DataMax), y(DataMin)), DataMax, (x(DataMin), y(DataMax))}) → viewbox
  5. Polygon({(-8, -11), (8, -11), (8, 11), (-8, 11)}) → pointBox
  6. KeepIf(IsInRegion[n, pointBox], n, PointsLine) → PointsLineFiltered
  7. Sequence(1, Length[PointsLineFiltered], If[Length[PointsLineFiltered] ≤ 8, 1, 2]) → possibleIndices
  8. Element(Remove[possibleIndices, {indexA}], 1 + floor((currentRandomSeeds(5) * (Length[possibleIndices] - 1)))) → indexB
  9. Element(Remove[possibleIndices, {indexA, indexB}], 1 + floor((currentRandomSeeds(6) * (Length[possibleIndices] - 2)))) → indexC
  10. Element(Remove[possibleIndices, {indexA, indexB, indexC}], 1 + floor((currentRandomSeeds(7) * (Length[possibleIndices] - 3)))) → indexD
  11. Sequence(PointsLineFiltered(sequenceUse(n)), n, 1, 4) → PointsUse
  12. KeepIf(n ≥ 0, n, xPoints) → xPointsPositive
  13. KeepIf(n < 0, n, xPoints) → xPointsNegative
  14. Sort(x(PointsUse)) → xPointsProblem
  15. Zip((A, (input1 * A)), A, xPointsProblem) → hintPointsAll
  16. Line(hintPointsAll(1), hintPointsAll(2)) → hintLine
  17. Zip(If[A < 0, (("(" * A) * ")"), ("" * A)], A, xPointsProblem) → displayXPoints
  18. RemoveUndefined({tempA}) → inputCurrent
  19. Textfield(input1) → InputBox1
  20. Segment((-11.5, 0), (11.5, 0)) → axisX
  21. Segment((0, -11.5), (0, 11.5)) → axisY
  22. Zip(Text[(("\bgcolor{WHITE}{" * A) * "}"), A + ((-5 * windowWidth / PXwindowWidth), (15 * windowHeight / PXwindowHeight)), true, true, 1, 0], A, PointsUse) → lblPoints
  23. Sort({Intersect[hintLine, viewbox]}) → hintEnds
  24. Polygon({DataMin, (x(DataMax), y(DataMin)), (x(DataMax), y(hintEnds(1) + vHint)), (x(DataMin), y(hintEnds(1) + vHint))}) → hintBoxA
  25. Polygon({DataMax, (x(DataMin), y(DataMax)), (x(DataMin), y(hintEnds(1) + vHint)), (x(DataMax), y(hintEnds(1) + vHint))}) → hintBoxB
  26. Polygon({DataMin, DataMin + vHint, (x(DataMin), y(DataMax)) + vHint, (x(DataMin), y(DataMax))}) → hintBoxC
  27. If(Slope[hintLine] < 0, hintBoxB, If[Slope[hintLine] ≟ 0, hintBoxC, hintBoxA]) → hintBox
  28. KeepIf(IsInRegion[A, hintBox], A, hintPointsAll) → hintPointsDisplay
  29. Segment(hintEnds(1), hintEnds(1) + vHint) → segmentHint
  30. IntersectPath(Line[PointsLine(1), PointsLine(2)], viewbox) → solnLine
  31. Segment(hintEnds(1), hintEnds(1) + vHint) → segmentCorrect
  32. If(showsolution, If[correct, {89 / 255, 145 / 255, 255 / 255}, {176 / 255, 0, 32 / 255}], {224 / 255, 116 / 255, 21 / 255}) → lineRGB
  33. If(showsolution, If[correct, {58 / 255, 110 / 255, 214 / 255}, {176 / 255, 0, 32 / 255}], {199 / 255, 80 / 255, 0}) → pointRGB

AI 绘图提示语参考

绘制一个坐标系，包含两条轴（X轴和Y轴）。在坐标系内绘制一条斜线作为提示线，并在该线附近标记一些点（xPointsProblem）。同时绘制一个输入框用于输入数字，以及一个解决方案线。坐标系边界为矩形，点线框为矩形。标签显示点坐标。提示线与坐标系边界相交，形成提示框。解决方案线与提示线平行或重合。整体图形用于演示乘法规则。
以上提示语为根据原始绘图命令整理而来，仅供参考。