命名移动：八年级几何变换入门（IM 8.1.2）

几何画板及绘图内容加载中，请稍等……

2020-07-20 22:53

数列解析几何变换几何作图

本范例是Illustrative Mathematics 8年级第1单元第2课的教学材料，主要演示如何用规范的数学语言命名和描述平面上的几何变换（平移、旋转、反射等）。它通过展示一组图形（如三角形及其像）在网格中的位置变化，引导学生观察并准确说出变换的类型和方向。核心数学概念包括几何变换、对应点、原像与像的关系，以及变换的符号表示。作图要点：使用GeoGebra的Point命令创建关键点（如A、B、C及其对应点A_1等），并用Sequence命令生成点列或图形序列，同时利用图片对象（pic1、pic2）作为背景或辅助说明，整体构造简洁直观。适合初中八年级学生学习几何变换的初步概念，也可用于教师课堂演示或学生自主探索，帮助建立从直观操作到抽象命名的过渡。

GeoGebra 命令及参数

Point(Circle[A_1, 5]) → B_1
Sequence(((6 * cos(θ°)), (6 * sin(θ°))), θ, 0, 359) → list1, {(6, 0), (5.999086170938348, 0.10471443862370107), (5.996344962114574, 0.2093969802150058), (5.991777208527443, 0.314015737457663), (5.985384301558945, 0.4185388424647518), (5.977168188550474, 0.522934456485949), (5.967131372209639, 0.6271707796059208), (5.955276909847932, 0.7312160604308848), (5.941608412449423, 0.8350386057603927), (5.926130043570827, 0.9386067902413853), (5.908846518073248, 1.041889066001582), (5.889763100685984, 1.1448539722592688), (5.868885604402834, 1.247470144906556), (5.846220388711411, 1.34970632606319), (5.821774357655979, 1.4515313735980064), (5.79555495773441, 1.5529142706151244), (5.767570175629913, 1.653824134901995), (5.737828535778212, 1.7542302283364206), (5.706339097770921, 1.8541019662496843), (5.673111453595901, 1.9534089267429402), (5.638155724715451, 2.0521208599540124), (5.601482558983211, 2.1502076972718016), (5.5631031274007245, 2.247639560495472), (5.523029120714642, 2.3443867709356425), (5.481272745855605, 2.4404198584548014), (5.437846722219899, 2.5357095704441965), (5.392764277795003, 2.6302268807344644), (5.346039145130208, 2.7239429984372805), (5.297685557153562, 2.816829376715345), (5.247718242836374, 2.9088577214780225), (5.196152422706632, 2.9999999999999996), (5.143003804212674, 3.0902284494603247), (5.088288576938556, 3.1795155853992294), (5.032023407672544, 3.2678342100901627), (4.97422543533025, 3.355157420824481), (4.914912265733951, 3.4414586181062763), (4.854101966249685, 3.526711513754839), (4.791813060283757, 3.6108901389122896), (4.728064521640332, 3.69396885195395), (4.662875768741825, 3.7759223462990246), (4.596266658713868, 3.8567256581192355), (4.528257481336632, 3.9363541739430437), (4.458868952864366, 4.014783638153149), (4.388122209715023, 4.091990160374991), (4.316038802031907, 4.1679502227539835), (4.242640687119286, 4.242640687119285), (4.1679502227539835, 4.316038802031907), (4.091990160374991, 4.388122209715023), 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(-0.6271707796059202, -5.96713137220964), (-0.5229344564859495, -5.977168188550474), (-0.4185388424647535, -5.985384301558945), (-0.31401573745766587, -5.991777208527443), (-0.20939698021500458, -5.996344962114574), (-0.10471443862370099, -5.999086170938348), (0, -6), (0.10471443862369878, -5.999086170938348), (0.2093969802150077, -5.996344962114574), (0.31401573745766365, -5.991777208527443), (0.4185388424647513, -5.985384301558946), (0.5229344564859473, -5.977168188550474), (0.6271707796059179, -5.96713137220964), (0.7312160604308862, -5.955276909847932), (0.8350386057603928, -5.941608412449423), (0.938606790241384, -5.926130043570827), (1.0418890660015798, -5.908846518073249), (1.1448539722592708, -5.889763100685983), (1.2474701449065566, -5.868885604402833), (1.3497063260631896, -5.846220388711411), (1.4515313735980047, -5.821774357655979), (1.5529142706151218, -5.79555495773441), (1.6538241349019964, -5.7675701756299125), (1.7542302283364202, -5.737828535778212), 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(4.014783638153147, -4.458868952864368), (4.0919901603749915, -4.388122209715022), (4.1679502227539835, -4.3160388020319065), (4.242640687119284, -4.242640687119286), (4.316038802031905, -4.167950222753985), (4.388122209715024, -4.09199016037499), (4.458868952864366, -4.0147836381531485), (4.528257481336631, -3.9363541739430445), (4.5962666587138665, -3.8567256581192373), (4.662875768741824, -3.7759223462990272), (4.7280645216403325, -3.693968851953949), (4.791813060283757, -3.6108901389122896), (4.854101966249684, -3.52671151375484), (4.91491226573395, -3.441458618106279), (4.974225435330251, -3.3551574208244794), (5.032023407672544, -3.267834210090162), (5.088288576938555, -3.17951558539923), (5.143003804212673, -3.090228449460327), (5.19615242270663, -3.0000000000000027), (5.247718242836375, -2.9088577214780216), (5.297685557153562, -2.816829376715345), (5.346039145130207, -2.723942998437282), (5.392764277795001, -2.6302268807344666), (5.4378467222199, -2.535709570444195), 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-0.10471443862370136)}
Point(Line[A, A + (1, 0)]) → B

AI 绘图提示语参考

画一个圆心在原点的圆，半径为5个单位长度。然后画一个从原点出发，沿x轴正方向延伸的线段，长度为1个单位长度。

以上提示语为根据原始绘图命令整理而来，仅供参考。