x轴与y轴反射练习游戏

x轴与y轴反射练习游戏
几何画板及绘图内容加载中,请稍等……
2021-01-18 21:24
该范例通过随机生成点与线段,让学习者练习把图形关于x轴、y轴进行反射并核对结果。核心数学概念包括:几何反射(轴对称)、全等、坐标几何中的对应点关系,以及反射后线段的对应位置与长度保持。作图与交互要点:使用RandomElement随机抽取元素,Sequence与Flatten生成点/线段候选列表,再用Shuffle与Take打乱与选取;通过Point、Segment构造原始点与线段,并用If进行条件判断(例如反射后生成的新对象选择与判分);同时设置列表对象与界面交互元素(如button1、score、level与text3/text4/text5)以实现分级与计分。适合中学数学(几何变换/坐标几何)课堂演示、课后练习与分层学习,也可用于培养空间想象与变换推理能力。

GeoGebra 命令及参数

  1. RandomElement(listRA) → refax, "j"
  2. Sequence(Sequence[(i, j), i, -10, 10], j, -10, 10) → listT
  3. Flatten(listT) → listR
  4. Shuffle(listR) → listS, {(-10, 2), (-1, 9), (-10, 1), (-2, -1), (-9, -5), (4, -3), (-2, -7), (9, 1), (9, -6), (4, -10), (-2, -3), (-5, -6), (-7, -9), (0, 3), (-7, 3), (9, 5), (10, -6), (6, 7), (6, -5), (-8, 3), (1, 4), (-1, 8), (10, 5), (10, 1), (8, -7), (-9, -9), (2, 4), (1, -4), (-1, -8), (-3, -5), (-6, -3), (0, -6), (-3, 4), (7, 2), (-1, -9), (-5, 1), (3, -7), (-3, -1), (-4, -2), (1, 1), (-4, -6), (-4, -3), (9, 7), (9, -8), (-3, 8), (3, 3), (6, -3), (-6, -8), (10, 0), (3, 9), (-9, -6), (-6, 6), (-7, -10), (9, -7), (-3, -8), (9, -9), (2, 3), (8, 10), (-10, -8), (0, 2), (3, 2), (8, 8), (-7, -5), (-1, 3), (3, -6), (-9, -2), (-8, -2), (6, -2), (-6, 3), (10, -10), (-1, 0), (-1, -6), (-5, -7), (2, 6), (-10, 3), (-4, 4), (-7, 0), (-6, 5), (5, 2), (-1, -7), (-5, 2), (-8, 1), (7, -5), (3, 4), (8, -9), (8, 4), (7, -1), (2, 0), (3, -1), (-5, 10), (8, -5), (-9, -3), (10, -4), (10, -1), (-2, 2), (-5, -2), (-3, 5), (0, 5), (5, 8), (-1, 10), (9, -4), (-4, 9), (0, -3), (6, -6), (-7, -1), (6, 10), (1, 6), (3, -9), (9, -10), (5, -4), (-8, -1), (-7, -6), (-10, 4), (4, 3), (1, -2), (-8, -7), (6, 9), (5, -1), (8, -4), (9, -2), (2, 2), (6, -4), (-4, -4), (-8, 8), (-1, -2), (-9, 1), (2, 10), (1, -5), (6, 1), (-7, 2), (10, 7), (-6, -6), (0, 7), (5, -9), (10, 9), (-5, 5), (-7, 9), (-10, -9), (8, -2), (-4, 5), (-5, -5), (10, 4), (4, -2), (-10, -4), (4, 1), (-9, 3), (4, -5), (-4, -8), (-3, 3), (-6, -7), (-3, -6), (0, -2), (4, 10), (7, 7), (-3, 1), (-6, 9), (0, -1), (9, 0), (6, 4), (10, 8), (0, -10), (5, -5), (8, 6), (5, -6), (6, 2), (-6, 1), (-1, 4), (6, -7), (-1, 2), (-8, 0), (-8, 4), (5, 7), (-6, 10), (-8, -5), (-7, -2), (-4, -1), (-1, 7), (-3, -4), (-8, 10), (-9, 6), (-9, 4), (-2, 5), (-2, 10), (8, -8), (-1, -3), (-5, 7), (9, 3), (2, -10), (7, 4), (9, 2), (-3, -2), (-2, -9), (3, 1), (-10, 7), (-6, -5), (-6, 4), (-2, 3), (2, 5), (-7, 6), (8, -6), (9, -5), (7, -2), (-5, 8), (-5, -3), (0, 0), (-1, 1), (10, 3), (2, -9), (-8, -9), (-2, -2), (6, 6), (5, 9), (1, 5), (2, 9), (-2, 0), (-10, -7), (9, 10), (2, -1), (6, -8), (1, -9), (3, -10), (9, -1), (5, 6), (7, -4), (8, -10), (0, -8), (2, 8), (-9, -7), (4, -7), (-10, 6), (10, -8), (9, 8), (-7, 8), (4, -4), (9, -3), (10, -5), (4, 7), (-8, -6), (3, -8), (8, 7), (-4, 2), (-7, 10), (-10, -2), (1, -7), (-5, -1), (1, 10), (5, 3), (-6, -4), (-5, -10), (10, 2), (7, -8), (7, 10), (-8, 6), (0, 1), (1, 2), (-3, 6), (0, 8), (7, -9), (5, 0), (-10, 0), (-10, 9), (8, 0), (-2, 4), (-6, 2), (-9, -4), (8, 3), (1, -6), (6, 5), (10, -7), (-7, -3), (0, -5), (-4, -5), (-7, -8), (3, -5), (-7, -4), (10, -2), (5, 4), (1, 0), (7, -7), (-2, 8), (-7, 7), (-2, 1), (6, -9), (-3, 7), (9, 6), (-6, -1), (-8, 5), (0, 10), (-9, 2), (-8, -4), (1, 8), (-2, -5), (-4, 8), (3, -3), (-8, 9), (-3, -3), (4, -1), (7, 6), (4, -8), (3, 10), (-10, -10), (-3, 10), (7, 0), (2, -7), (5, -7), (4, 9), (-5, -4), (-7, -7), (-7, 5), (-2, -6), (5, 5), (-5, 9), (-7, 1), (-5, -8), (2, -8), (-9, -10), (-6, -9), (1, 3), (10, 6), (8, 5), (-10, -3), (-2, -8), (4, -9), (-5, 6), (0, -4), (7, 1), (1, -8), (-9, -8), (7, 5), (6, 0), (-5, -9), (-8, -8), (-9, 7), (10, 10), (3, 5), (5, -3), (-8, -3), (-1, -4), (2, 1), (-10, -1), (-2, -10), (-1, -10), (9, 4), (-8, 7), (7, -3), (-4, 1), (-5, 3), (5, -10), (-4, 6), (8, -3), (3, 8), (-3, -9), (1, -3), (-2, 6), (7, -10), (9, 9), (-10, -5), (-5, 0), (-8, -10), (-3, 2), (0, -9), (-6, 0), (8, 1), (4, 2), (8, 2), (-4, -9), (-2, -4), (-8, 2), (-9, 0), (1, 7), (-4, 0), (0, 6), (-9, -1), (7, 9), (-1, 5), (-9, 5), (2, -6), (-4, -7), (2, -3), (4, -6), (1, -10), (-6, 8), (-3, 0), (4, 6), (4, 0), (1, 9), (10, -3), (5, 10), (0, 4), (2, 7), (6, -1), (5, 1), (4, 4), (-6, 7), (3, -4), (3, 6), (-1, -1), (-3, -10), (-9, 8), (-4, -10), (-10, -6), (-4, 10), (-6, -2), (-1, 6), (8, -1), (5, -2), (-7, 4), (7, 8), (-2, 7), (2, -4), (-10, 10), (3, -2), (8, 9), (-10, 5), (3, 0), (7, -6), (6, 3), (-9, 10), (-5, 4), (-9, 9), (2, -2), (-3, 9), (-2, 9), (-4, 3), (7, 3), (6, -10), (-6, -10), (4, 5), (1, -1), (-4, 7), (0, 9), (4, 8), (3, 7), (-10, 8), (-1, -5), (10, -9), (0, -7), (6, 8), (2, -5), (-3, -7), (5, -8)}
  5. Take(listS, 1, 1) → listA
  6. Point(listA) → A
  7. Take(listS, 4, 4) → listD
  8. Point(listD) → D
  9. Take(listS, 5, 5) → listE
  10. Point(listE) → E
  11. Take(listS, 6, 6) → listF
  12. Point(listF) → F
  13. Take(listS, 3, 3) → listC
  14. Point(listC) → C
  15. Take(listS, 2, 2) → listB
  16. Point(listB) → B
  17. Segment(A, B) → ab
  18. Segment(B, C) → bc
  19. Segment(C, A) → ca
  20. Segment(A', B') → a'b'
  21. Segment(B', C') → b'c'
  22. Segment(C', A') → c'a'
  23. Segment(C, D) → cd
  24. Segment(D, A) → da
  25. Segment(D, E) → de
  26. Segment(E, A) → ea
  27. Segment(E, F) → ef
  28. Segment(F, A) → fa
  29. Segment(C', D') → c'd'
  30. Segment(D', E') → d'e'
  31. Segment(E', F') → e'f'
  32. Segment(F', A') → f'a'
  33. Segment(E', A') → e'a'
  34. Segment(D', A') → d'a'
  35. RandomElement({"Awesome!", "Great Job!", " Correct!"}) → praise, " Correct!"
  36. If(refax ≟ "j", "x", If[refax ≟ "k", "y", If[refax ≟ "l", "x - axis and y"]]) → axis
  37. If(refax ≟ "j", (x(A), (-y(A))), If[refax ≟ "k", ((-x(A)), y(A)), If[refax ≟ "l", ((-x(A)), (-y(A)))]]) → U
  38. If(refax ≟ "j", (x(B), (-y(B))), If[refax ≟ "k", ((-x(B)), y(B)), If[refax ≟ "l", ((-x(B)), (-y(B)))]]) → V
  39. If(refax ≟ "j", (x(C), (-y(C))), If[refax ≟ "k", ((-x(C)), y(C)), If[refax ≟ "l", ((-x(C)), (-y(C)))]]) → W
  40. If(refax ≟ "j", (x(D), (-y(D))), If[refax ≟ "k", ((-x(D)), y(D)), If[refax ≟ "l", ((-x(D)), (-y(D)))]]) → X
  41. If(refax ≟ "j", (x(E), (-y(E))), If[refax ≟ "k", ((-x(E)), y(E)), If[refax ≟ "l", ((-x(E)), (-y(E)))]]) → Y
  42. If(refax ≟ "j", (x(F), (-y(F))), If[refax ≟ "k", ((-x(F)), y(F)), If[refax ≟ "l", ((-x(F)), (-y(F)))]]) → Z

AI 绘图提示语参考

在坐标系中绘制一个由四点组成的三角形组:从预先选取的6个整数坐标点里取5个点来作图,得到点A、B、C形成三角形AB、BC、CA三条线段;再用点D、E、F分别与A、C构成附加线段CD、DA,以及从D、E、F到A的线段DE、EA、EF、FA,并确保这些线段都是端点相连的直线线段。再在同一坐标系中再放置对应的关于坐标轴反射后的点A’、B’、C’、D’、E’、F’,并绘制反射后的三条三角形边A’B’、B’C’、C’A’,以及反射后的线段C’D’、D’E’、E’F’、F’A’、E’A’、D’A’。
以上提示语为根据原始绘图命令整理而来,仅供参考。