Transformation Demo

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2020-10-23 18:57

This example demonstrates transformations like reflection, rotation, and translation of points, polygons, and images in a 2D plane. It involves core math concepts such as transformation, coordinate geometry, vectors, and geometric construction. Key GeoGebra commands used include Polygon, AttachCopyToView, and objects like A-E, poly1, a-b. Suitable for high school mathematics teaching to visually understand the properties and operations of geometric transformations.

GeoGebra Commands & Parameters

Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
AttachCopyToView(PolyLine[(10.492204631523343, 0.4152902229014462), (10.473673754500354, 0.359697591832477), (10.455142877477364, 0.3041049607635078), (10.399550246408396, 0.26704320671752835), (10.362488492362415, 0.21145057564855912), (10.306895861293446, 0.17438882160257968), (10.251303230224478, 0.15585794457958993), (10.195710599155507, 0.11879619053361047), (10.12158709106355, 0.10026531351062073), (10.06599445999458, 0.08173443648763101), (9.973340074879632, 0.08173443648763101), (9.917747443810661, 0.06320355946464128), (9.843623935718703, 0.06320355946464128), (9.788031304649735, 0.04467268244165154), (9.713907796557775, 0.04467268244165154), (9.658315165488807, 0.06320355946464128), (9.602722534419836, 0.10026531351062073), (9.547129903350868, 0.11879619053361047), (9.4915372722819, 0.1373270675566002), (9.435944641212929, 0.17438882160257968), (9.38035201014396, 0.22998145267154887), (9.324759379074992, 0.3041049607635078), (9.269166748006022, 0.3411667148094873), (9.213574116937053, 0.39675934587845646), (9.195043239914064, 0.4523519769474257), (9.139450608845094, 0.5079446080163948), (9.120919731822104, 0.563537239085364), (9.083857977776125, 0.6191298701543333), (9.065327100753136, 0.6747225012233025), (9.028265346707157, 0.7303151322922716), (9.028265346707157, 0.8044386403842306), (9.009734469684167, 0.8600312714531998), (9.009734469684167, 0.9526856565681484), (9.009734469684167, 1.0268091646601074), (9.009734469684167, 1.119463549775056), (9.009734469684167, 1.193587057867015), (9.028265346707157, 1.2677105659589738), (9.065327100753136, 1.341834074050933), (9.102388854799115, 1.397426705119902), (9.157981485868085, 1.4530193361888712), (9.232104993960043, 1.4900810902348507), (9.306228502052, 1.5086119672578404), (9.361821133120971, 1.5271428442808301), (9.41741376418994, 1.5642045983268096), (9.4915372722819, 1.5642045983268096), (9.565660780373857, 1.5642045983268096), (9.639784288465817, 1.5642045983268096), (9.713907796557775, 1.5642045983268096), (9.788031304649735, 1.5642045983268096), (9.843623935718703, 1.5456737213038199), (9.899216566787672, 1.5086119672578404), (9.954809197856642, 1.471550213211861), (10.01040182892561, 1.4530193361888712), (10.04746358297159, 1.397426705119902), (10.10305621404056, 1.3603649510739226), (10.12158709106355, 1.3047723200049535), (10.158648845109528, 1.249179688935984), (10.177179722132518, 1.1750561808440252), (10.214241476178497, 1.119463549775056), (10.232772353201486, 1.0638709187060869), (10.251303230224478, 1.0082782876371177), (10.269834107247467, 0.9341547795451587), (10.288364984270457, 0.8600312714531998), (10.306895861293446, 0.8044386403842306), (10.325426738316436, 0.8600312714531998), (10.325426738316436, 0.9341547795451587), (10.325426738316436, 1.0082782876371177), (10.325426738316436, 1.0824017957290766), (10.288364984270457, 1.1379944267980457), (10.269834107247467, 1.193587057867015), (10.251303230224478, 1.249179688935984), (10.214241476178497, 1.3047723200049535), (10.214241476178497, 1.3788958280969124), (10.214241476178497, 1.4530193361888712), (10.214241476178497, 1.5271428442808301), (10.214241476178497, 1.601266352372789), (10.214241476178497, 1.6753898604647481), (10.214241476178497, 1.749513368556707), (10.232772353201486, 1.823636876648666), (10.251303230224478, 1.8977603847406248), (10.288364984270457, 1.9718838928325837), (10.325426738316436, 2.027476523901553), (10.343957615339425, 2.0830691549705223), (10.399550246408396, 2.157192663062481), (10.436612000454375, 2.21278529413145), (10.492204631523343, 2.2683779252004195), (10.529266385569322, 2.323970556269389), (10.584859016638292, 2.379563187338358), (10.64045164770726, 2.435155818407327), (10.67751340175324, 2.490748449476296), (10.73310603282221, 2.5278102035222756), (10.788698663891179, 2.564871957568255), (10.844291294960147, 2.6019337116142345), (10.881353049006128, 2.657526342683204), (10.936945680075096, 2.676057219706194), (10.992538311144065, 2.6945880967291833), (11.048130942213035, 2.7131189737521733), (11.122254450304993, 2.7131189737521733), (11.196377958396953, 2.6945880967291833), (11.2890323435119, 2.6945880967291833), (11.36315585160386, 2.657526342683204), (11.437279359695818, 2.638995465660214), (11.511402867787778, 2.6204645886372244), (11.566995498856746, 2.6019337116142345), (11.622588129925715, 2.583402834591245), (11.678180760994685, 2.564871957568255), (11.733773392063654, 2.5463410805452655), (11.789366023132622, 2.5278102035222756), (11.844958654201593, 2.4722175724533066), (11.863489531224582, 2.4166249413843373), (11.882020408247572, 2.3610323103153683), (11.882020408247572, 2.2869088022234094), (11.882020408247572, 2.21278529413145), (11.882020408247572, 2.1201309090165017), (11.882020408247572, 2.046007400924543), (11.882020408247572, 1.9718838928325837), (11.863489531224582, 1.9162912617636145), (11.826427777178603, 1.8606986306946454), (11.807896900155614, 1.8051059996256762), (11.770835146109633, 1.749513368556707), (11.733773392063654, 1.6939207374877379), (11.678180760994685, 1.6383281064187685), (11.622588129925715, 1.5827354753497993), (11.585526375879736, 1.5271428442808301), (11.548464621833757, 1.471550213211861), (11.492871990764788, 1.4344884591658815), (11.437279359695818, 1.397426705119902), (11.40021760564984, 1.341834074050933), (11.34462497458087, 1.3233031970279432), (11.30756322053489, 1.2677105659589738), (11.251970589465921, 1.2306488119129944), (11.196377958396953, 1.193587057867015), (11.140785327327983, 1.1379944267980457), (11.085192696259014, 1.1009326727520663), (11.029600065190046, 1.0638709187060869), (10.974007434121075, 1.0268091646601074), (10.918414803052107, 0.989747410614128), (10.862822171983137, 0.9526856565681484), (10.807229540914168, 0.9341547795451587), (10.7516369098452, 0.915623902522169), (10.69604427877623, 0.8785621484761895), (10.64045164770726, 0.8600312714531998), (10.584859016638292, 0.8785621484761895), (10.64045164770726, 0.9341547795451587), (10.69604427877623, 0.9526856565681484), (10.7516369098452, 0.9712165335911381), (10.825760417937158, 0.989747410614128), (10.881353049006128, 1.0082782876371177), (10.936945680075096, 1.0268091646601074), (10.992538311144065, 1.0453400416830971), (11.066661819236025, 1.0453400416830971), (11.122254450304993, 1.0638709187060869), (11.177847081373963, 1.0824017957290766), (11.270501466488911, 1.0824017957290766), (11.34462497458087, 1.1009326727520663), (11.418748482672829, 1.1009326727520663), (11.511402867787778, 1.1009326727520663), (11.585526375879736, 1.1009326727520663), (11.678180760994685, 1.1009326727520663), (11.752304269086643, 1.1009326727520663), (11.826427777178603, 1.1009326727520663), (11.882020408247572, 1.0824017957290766), (11.93761303931654, 1.0638709187060869), (11.99320567038551, 1.0453400416830971), (12.048798301454479, 0.989747410614128), (12.104390932523447, 0.9341547795451587), (12.141452686569428, 0.8785621484761895), (12.178514440615407, 0.8229695174072204), (12.197045317638397, 0.7673768863382511), (12.215576194661386, 0.7117842552692819), (12.234107071684376, 0.6561916242003127), (12.234107071684376, 0.5820681161083537), (12.234107071684376, 0.5079446080163948), (12.234107071684376, 0.4338210999244359), (12.197045317638397, 0.37822846885546674), (12.141452686569428, 0.3226358377864975), (12.067329178477468, 0.28557408374051807), (12.0117365474085, 0.2485123296945386), (11.956143916339531, 0.22998145267154887), (11.900551285270561, 0.1929196986255694), (11.826427777178603, 0.17438882160257968), (11.752304269086643, 0.17438882160257968), (11.678180760994685, 0.17438882160257968), (11.622588129925715, 0.15585794457958993), (11.548464621833757, 0.15585794457958993), (11.474341113741797, 0.15585794457958993), (11.40021760564984, 0.15585794457958993), (11.32609409755788, 0.15585794457958993), (11.251970589465921, 0.15585794457958993), (11.177847081373963, 0.17438882160257968), (11.103723573282004, 0.17438882160257968), (11.048130942213035, 0.21145057564855912), (10.974007434121075, 0.21145057564855912), (10.918414803052107, 0.22998145267154887), (10.862822171983137, 0.2485123296945386), (10.807229540914168, 0.26704320671752835), (10.7516369098452, 0.28557408374051807), (10.69604427877623, 0.3041049607635078), (10.64045164770726, 0.3226358377864975), (10.584859016638292, 0.3411667148094873), (10.529266385569322, 0.37822846885546674), (10.510735508546333, 0.3226358377864975), (10.492204631523343, 0.26704320671752835), (10.492204631523343, 0.1929196986255694), (10.473673754500354, 0.1373270675566002), (10.455142877477364, 0.06320355946464128), (10.455142877477364, -0.010919948627317658), (10.436612000454375, -0.06651257969628685), (10.418081123431385, -0.15916696481123552), (10.399550246408396, -0.2147595958802047), (10.399550246408396, -0.3259448580181431), (10.381019369385404, -0.3815374890871123), (10.362488492362415, -0.45566099717907127), (10.343957615339425, -0.5297845052710302), (10.343957615339425, -0.6224388903859789), (10.325426738316436, -0.6965623984779378), (10.325426738316436, -0.7892167835928864), (10.325426738316436, -0.8633402916848454), (10.306895861293446, -0.9189329227538146), (10.306895861293446, -1.0115873078687632), (10.306895861293446, -1.1227725700067017), (10.306895861293446, -1.23395783214464), (10.325426738316436, -1.3451430942825784), (10.343957615339425, -1.4007357253515476), (10.362488492362415, -1.5119209874894861), (10.399550246408396, -1.6231062496274244), (10.418081123431385, -1.6972297577193833), (10.455142877477364, -1.7713532658113422), (10.473673754500354, -1.8269458968803114), (10.529266385569322, -1.9196002819952602), (10.547797262592312, -1.9937237900872191), (10.603389893661282, -2.067847298179178), (10.621920770684271, -2.123439929248147), (10.65898252473025, -2.197563437340106), (10.71457515579922, -2.2531560684090755), (10.770167786868189, -2.3272795765010343), (10.807229540914168, -2.3828722075700033), (10.844291294960147, -2.4384648386389727), (10.899883926029117, -2.5125883467309316), (10.974007434121075, -2.5867118548228905), (11.048130942213035, -2.6608353629148493), (11.103723573282004, -2.7164279939838187), (11.159316204350972, -2.753489748029798), (11.214908835419942, -2.7720206250527877), (11.251970589465921, -2.827613256121757), (11.32609409755788, -2.8461441331447466), (11.38168672862685, -2.8646750101677365), true], 1, (-2.6091254237303825, -11.611248965018891), (28.522747974892333, 5.344503511016715), (81.34524396600321, 1041.5892839617775), (1761.3452439660036, 126.58928396177728)) → stroke1

AI Drawing Prompt Reference

Draw a 2D plane containing a polygon with five vertices and a complex polyline curve formed by numerous connected points. The curve appears as an irregular closed or decorative shape with many twists and turns, independent from the polygon. Both objects should be clearly visible in the same coordinate system, suitable for demonstrating geometric transformations such as translation, rotation, or reflection. The overall composition should emphasize the spatial relationships between the polygon and the intricate curve.

The prompt above was compiled from the original drawing commands and is for reference only.