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Find Multiplication Rule for Points on a Line

Find Multiplication Rule for Points on a Line
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2023-08-10 10:31
FunctionSequenceCoordinate Geometry
This example demonstrates how to find the multiplication rule for points on a line. Key mathematical concepts include linear functions in coordinate geometry. GeoGebra commands used include Line, Sequence, KeepIf, etc. Suitable for 6-8 grade students.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a coordinate system with X and Y axes. Draw a diagonal line as a hint line. Mark some points (xPointsProblem) near the line. Include an input box for entering numbers and a solution line. The coordinate system is bounded by a rectangle, and points are shown within it. Labels display point coordinates. The hint line intersects the boundary to form a hint box. The solution line is parallel or coincident with the hint line. The overall figure demonstrates the multiplication rule. The points are randomly generated and filtered to ensure they are within the coordinate system. The hint line helps users visualize the relationship between points and the line. The solution line indicates the correct multiplication result.
The prompt above was compiled from the original drawing commands and is for reference only.