几何平移练习游戏：同形变换与得分判定

几何画板及绘图内容加载中，请稍等……

2021-01-10 00:27

向量函数数列变换几何作图

本范例通过交互式“平移练习游戏”展示几何图形在坐标平面中的平移后仍保持形状与距离关系的现象。核心数学概念包括：全等（congruence）、几何变换（translation）、点与线段的对应、以及用距离/条件判断来验证学生给出的平移是否正确（可与函数/统计式得分或置信区间思想结合）。作图与实现要点：利用 Sequence 生成坐标点序列；借助 Flatten/Shuffle/Take 构造并随机选取练习目标与参数；用 Point 与 Segment 创建原图和变换后的几何元素；使用 Distance 计算关键点或线段的误差；结合 If 与 RandomElement 根据误差阈值给出正确/错误与积分（score）。相关对象包括 listT、listR、listA 等参数列表、以及 A、B、C 等点和 A'、B'、C' 等平移后的对应点，配套按钮 button1 与文本 text1~text5 展示关键信息与难度 level。适合初中到高中几何与坐标几何教学，适用于课堂练习、能力检测或自学中的几何变换训练。

GeoGebra 命令及参数

Sequence(Sequence[(i, j), i, -10, 10], j, -10, 10) → listT
Flatten(listT) → listR
Shuffle(listR) → listS, {(1, 2), (-5, 5), (1, 8), (7, 0), (-5, -3), (4, 6), (-5, 6), (7, -5), (10, 8), (0, -8), (6, -3), (-10, 8), (-1, 0), (8, -4), (2, 4), (1, 0), (-3, -3), (-7, 9), (-3, -10), (-8, -4), (0, 4), (-1, -9), (-8, -3), (0, 6), (-3, 6), (-3, 8), (2, 10), (2, -4), (1, -8), (-3, -1), (5, -1), (10, 2), (6, -9), (-8, 0), (0, 2), (-9, -1), (-2, -9), (3, 10), (-9, -3), (-10, 7), (-9, 7), (8, 0), (8, -5), (0, 3), (-9, -9), (3, -6), (-2, 10), (-5, -9), (-4, 4), (5, -9), (8, 6), (0, -2), (-9, 4), (-10, 9), (7, 2), (-7, -3), (2, 3), (-5, -7), (-2, 6), (-2, -6), (-2, 4), (-7, -2), (4, 4), (-6, -5), (8, 9), (6, 8), (3, 8), (-10, -7), (-6, -8), (-1, -10), (4, 0), (-6, 9), (-5, -6), (-10, -3), (4, 9), (9, 10), (1, -4), (-6, 8), (1, -6), (3, -9), (10, 4), (3, -5), (8, 5), (10, 9), (-2, 2), (-8, -10), (-5, -8), (-5, 3), (-1, -5), (7, -3), (3, 7), (2, 7), (-2, -1), (-10, -4), (8, -10), (5, 0), (1, -7), (-2, 7), (-4, 6), (-10, -1), (5, 1), (-1, -3), (-10, 5), (-9, 3), (3, 0), (0, -4), (-7, -4), (-7, -5), (-6, 2), (6, -6), (-1, 10), (2, 5), (-1, 3), (2, 2), (4, -6), (4, -9), (7, 5), (-4, 7), (-2, -4), (-8, 10), (8, -2), (3, -1), (-8, 6), (4, 8), (-8, -8), (2, -9), (3, 1), (-3, -4), (5, 5), (9, 4), (-9, 10), (6, 9), (0, 8), (6, 3), (10, -9), (-10, 10), (-4, 1), (-4, -3), (-9, 9), (6, -1), (-7, 0), (3, 2), (3, -8), (9, 1), (-4, 10), (10, -8), (0, 5), (10, 7), (1, 6), (-5, 8), (5, -10), (9, -7), (-6, 3), (-2, -5), (7, 7), (-2, 1), (6, 5), (-8, -7), (2, 6), (-10, -2), (-8, -2), (-8, 9), (-1, 9), (-8, 8), (-4, -10), (2, -7), (-7, 4), (1, 4), (7, -6), (2, -1), (0, -7), (-3, 2), (9, -6), (-5, -1), (10, -6), (7, 9), (-6, -6), (10, -2), (-6, 0), (-3, -8), (2, -10), (4, -8), (3, 6), (-6, 10), (8, 10), (5, 2), (-3, 0), (0, 10), (2, -3), (-3, -6), (10, -5), (7, 8), (0, -6), (4, -3), (-4, 3), (-7, 8), (1, 5), (1, 9), (-6, -7), (1, 7), (0, 0), (-1, -8), (5, 8), (1, -9), (-8, -9), (-1, -4), (-4, -5), (9, 5), (4, 10), (1, -3), (-3, 7), (3, -3), (2, 9), (-8, -1), (4, -1), (-7, 7), (10, -10), (-10, 3), (-4, 9), (-3, 4), (-7, -8), (10, -1), (-3, -5), (-6, -2), (-3, -9), (-3, 1), (-9, -6), (-9, -5), (6, 0), (-8, 3), (-6, -3), (10, 6), (-2, 0), (-6, 1), (-7, -6), (4, -2), (9, 8), (-4, -9), (6, -7), (-10, 4), (-2, -8), (-6, -10), (-4, -2), (2, -6), (-10, -10), (-1, 1), (-8, -6), (5, -8), (9, -3), (5, -2), (-4, -8), (-6, 6), (7, -1), (-3, 10), (6, 2), (4, 5), (6, 4), (8, 2), (4, 7), (-4, -4), (3, -10), (9, 0), (-9, 0), (-2, -3), (1, 10), (1, 1), (-8, 1), (-5, -4), (-4, 0), (8, 1), (10, -3), (9, -8), (1, -5), (-3, -7), (-6, 7), (-2, 9), (-7, 3), (-5, 9), (4, 2), (-3, -2), (-1, 6), (-8, 4), (-5, 10), (3, 3), (0, -9), (-9, -7), (-1, -7), (5, 9), (-8, 2), (-2, 5), (5, -5), (2, -8), (-1, 4), (-7, -1), (3, -2), (-8, -5), (6, 10), (0, -1), (5, 7), (3, 5), (7, -4), (8, -8), (5, 4), (5, 10), (7, 1), (9, 2), (7, 3), (6, -8), (8, -1), (-9, -4), (5, -7), (7, 6), (-1, 2), (3, -7), (0, 7), (0, 1), (5, -4), (6, 6), (-7, -9), (8, -6), (10, 1), (3, 9), (6, -10), (1, -2), (-4, 8), (-9, 1), (4, -7), (5, 6), (-7, 6), (-9, -2), (4, 1), (-3, 5), (6, -2), (-1, 7), (5, -3), (0, -5), (3, 4), (8, -7), (-9, 2), (-1, 8), (1, -10), (-10, -9), (-2, 8), (-6, -1), (2, -5), (8, 4), (-1, -6), (5, -6), (-6, 4), (6, -4), (-5, 4), (-5, -2), (-4, -7), (-7, 5), (-5, 0), (7, 4), (-3, 3), (-8, 5), (-9, 5), (10, -7), (4, -5), (-7, 2), (-3, 9), (9, 6), (10, 5), (2, 1), (-10, 1), (-10, -6), (8, -9), (-7, 1), (-4, -1), (-6, -9), (9, -4), (-2, -7), (-5, -5), (5, 3), (-5, 7), (-5, -10), (-5, 1), (-4, 5), (-10, 6), (-6, 5), (-2, -2), (-2, 3), (-9, 8), (1, -1), (2, 0), (9, 7), (0, -3), (-1, 5), (0, -10), (9, -10), (2, 8), (10, -4), (8, -3), (7, 10), (9, -1), (-5, 2), (1, 3), (10, 0), (-1, -2), (-10, 2), (2, -2), (0, 9), (-7, 10), (-10, -8), (7, -7), (7, -9), (9, -2), (9, -5), (-10, 0), (7, -2), (9, -9), (9, 3), (8, 8), (-4, -6), (8, 3), (6, 7), (-9, -8), (4, -4), (3, -4), (-7, -7), (-6, -4), (4, 3), (-9, 6), (8, 7), (9, 9), (-7, -10), (10, 10), (7, -8), (-1, -1), (-8, 7), (7, -10), (-9, -10), (6, -5), (6, 1), (4, -10), (-4, 2), (-2, -10), (10, 3), (-10, -5)}
Take(listS, 4, 4) → listD
Point(listD) → D
Take(listS, 4, 4) → listA'
Point(listA') → U
Take(listS, 1, 1) → listA
Point(listA) → A
Take(listS, 5, 5) → listE
Point(listE) → E
Take(listS, 6, 6) → listF
Point(listF) → F
Take(listS, 3, 3) → listC
Point(listC) → C
Take(listS, 2, 2) → listB
Point(listB) → B
Segment(A, B) → ab
Segment(B, C) → bc
Segment(C, A) → ca
Distance(X, Y) → XY
Segment(A', B') → a'b'
Segment(B', C') → b'c'
Segment(C', A') → c'a'
Segment(C, D) → cd
Segment(D, A) → da
Segment(D, E) → de
Segment(E, A) → ea
Segment(E, F) → ef
Segment(F, A) → fa
Segment(C', D') → c'd'
Segment(D', E') → d'e'
Segment(E', F') → e'f'
Segment(F', A') → f'a'
Segment(E', A') → e'a'
Segment(D', A') → d'a'
If(level ≟ 1, A' ≟ U, If[level ≟ 2, A' ≟ U ∧ B' ≟ V, If[level ≟ 3, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W, If[level ≟ 4, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W ∧ D' ≟ X, If[level ≟ 5, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W ∧ D' ≟ X ∧ E' ≟ Y, If[level ≥ 6, A' ≟ U ∧ B' ≟ V ∧ C' ≟ W ∧ D' ≟ X ∧ E' ≟ Y ∧ F' ≟ Z]]]]]) → correct
RandomElement({"Awesome!", "Great Job!", " Correct!"}) → praise, " Correct!"

AI 绘图提示语参考

在坐标平面上绘制一个平移练习游戏场景。首先随机生成一个包含多个整数坐标点的点集，从中选取六个点作为原始图形的顶点，并用线段连接它们构成一个六边形。再选取一个点作为平移目标点，将原始六边形整体平移，使其中一个顶点与目标点重合，得到平移后的六边形。同时，在原始图形中额外选取几个点，与原始顶点连接形成内部辅助线段，并在平移后的图形中对应画出这些辅助线。最后，根据平移后顶点与预设目标点的匹配情况，显示正确或鼓励性文字反馈，并设置一个按钮用于切换难度等级。

以上提示语为根据原始绘图命令整理而来，仅供参考。