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LR3-02-CYU2：判断两个线性表示是否等价

LR3-02-CYU2：判断两个线性表示是否等价
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2019-02-01 04:15
函数解析几何不等式几何作图滑块动画
该范例通过交互式练习，让学生判断两个线性表示（如线性方程组或线性变换的矩阵形式）是否等价。核心数学概念是线性表示、等价性以及线性方程组的解集比较。作图要点包括：使用GeoGebra的Polygon命令构建立方体或矩形区域，通过UnicodeToLetter和LaTeX生成数学符号，利用Random和If随机生成题目，用IsInRegion检测点是否在区域内，配合TableText展示数据，并通过按钮（如TryAnother）和反馈对象（如correct、incorrect）实现自测。适合高中或大学低年级线性代数课程，用于巩固线性表示等价性的判断方法。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → box, a, b, c, d_1
  2. UnicodeToLetter(10007) → xmark
  3. UnicodeToLetter(10003) → cmark
  4. Polygon(anchorEquivalent, anchorEquivalent + (widthOfEquivalent, 0), anchorEquivalent + (widthOfEquivalent, (-heightOfEquivalent)), anchorEquivalent + (0, (-heightOfEquivalent))) → dragBoxEquivalent, f, g, h, i
  5. Polygon(anchorNotEquivalent, anchorNotEquivalent + (widthOfNotEquivalent, 0), anchorNotEquivalent + (widthOfNotEquivalent, (-heightOfNotEquivalent)), anchorNotEquivalent + (0, (-heightOfNotEquivalent))) → dragBoxNotEquivalent, j, k, l, m
  6. IsInRegion(midAnchorEquivalent, box) → isEquivalentInRegion
  7. IsInRegion(midAnchorNotEquivalent, box) → isNotEquivalentInRegion
  8. If(Random[0, 1] ≟ 0, Random[-4, -1], Random[1, 4]) → slope1
  9. Random(-5, 5) → intercept1
  10. Random(0, 1) → samenessIndicator
  11. If(samenessIndicator ≟ 0, slope1, If[Random[0, 1] ≟ 0, Random[-4, -1], Random[1, 4]]) → slope2
  12. If(samenessIndicator ≟ 0, intercept1, Random[-5, 5]) → intercept2
  13. Zip(line1(A), A, xValues) → yValues1
  14. Zip(line2(A), A, xValues) → yValues2
  15. TableText({Join[{{LaTeX["\cellcolor{#ffcc80}{x}"]}, xValues}], Join[{{LaTeX["\cellcolor{#ffcc80}{y}"]}, yValues1}]}, "|_vc") → table1
  16. TableText({Join[{{LaTeX["\cellcolor{#ffcc80}{x}"]}, xValues}], Join[{{LaTeX["\cellcolor{#ffcc80}{y}"]}, yValues2}]}, "|_vc") → table2
  17. LaTeX(("y=" * Polynomial[line1])) → equation1
  18. LaTeX(("y=" * Polynomial[line2])) → equation2
  19. Random(1, 4) → type
  20. LaTeX((((((((((("\text{The two representations are of the same linear relation if they\\have identical values for the slope and \(y\)-intercept. The first representation has a\\slope of \(" * slope1) * "\) and a \(y\)-intercept of \(") * intercept1) * "\). The second representation has a slope of \(") * slope2) * "\) and a\\\(y\)-intercept of \(") * intercept2) * "\). \textbf{Therefore, they are ") * If[¬areSame, "not ", ""]) * "equivalent.}}")) → feedback
  21. LaTeX("\text{Please drag a phrase into the box.}") → errorNoneDragged
  22. LaTeX("\text{Only drag one phrase into the box.}") → errorBothDragged
  23. LaTeX("\text{\textbf{Question: }Are these two linear representations equivalent?\\\textbf{Instructions: }Determine if the two representations are of the same linear relation,\\and then drag the appropriate phrase into the box.}") → TEXT

AI 绘图提示语参考

绘制一个包含两个线性方程表格的交互式教学图形。左侧显示两个数据表，分别列出x值及对应的y值，右侧显示两个线性方程及其斜率与截距。下方设置两个拖拽区域，分别标记为“等价”和“不等价”，用于学生判断两个线性表示是否等价。图形背景为矩形区域，包含随机生成的直线方程，并配有反馈文字说明判断结果。整体布局清晰，适合课堂练习。
以上提示语为根据原始绘图命令整理而来，仅供参考。