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Demonstration of Equivalent Linear Equations in GeoGebra

Demonstration of Equivalent Linear Equations in GeoGebra
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2019-03-15 02:47
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically illustrates the geometric meaning and correspondence of solutions for equivalent linear equations using GeoGebra. It involves core mathematical concepts such as linear equations, equivalence, conditional probability, cylinders, polygons, and polynomial functions. The construction summary leverages commands like Element, LaTeX, Text, questionList, questionNum, cmark, TryAnother, HowDidIDo, Initialize, numQuestions, copyright, xmark, isChecked, incorrectLeftPiece, correctLeftPiece, incorrectRightPiece, correctRightPiece, A1, puzzleAnchor, allMatched, isRightMatched, isLeftMatched, correctLeftVisible, correctRightVisible, incorrectLeftVisible, incorrectRightVisible, B1, C1, D1, E1, correctRightText, correctLeftText, incorrectRightText, incorrectLeftText, startingPlaces, isLeftCorrect, isRightCorrect. It is suitable for high school mathematics education to understand the determination and visualization of solutions for systems of linear equations.

GeoGebra Commands & Parameters

  1. Element(questionList, questionListIndex) → questionNum
  2. LaTeX(UnicodeToLetter[10003]) → cmark
  3. LaTeX(UnicodeToLetter[10007]) → xmark
  4. Element(C2:C6, questionNum) → correctRightText
  5. Element(B2:B6, questionNum) → correctLeftText
  6. Element(E2:E6, questionNum) → incorrectRightText
  7. Element(D2:D6, questionNum) → incorrectLeftText
  8. Element(A2:A6, questionNum) → questionText
  9. Element(F2:F6, questionNum) → feedback
  10. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  11. LaTeX("y=-4x-7") → A2
  12. LaTeX("3x-y+11=0") → A3
  13. LaTeX("4x\!+\!y\!+\!7\!=\!0") → C2
  14. LaTeX("3x\!-\!y\!=\!-11") → C3
  15. LaTeX("10x\!-\!y\!-\!9\!=\!0") → C4
  16. LaTeX("y\!=\!-8x\!+\!5") → C5
  17. LaTeX("10x=y+9") → A4
  18. LaTeX("8x+y=5") → A5
  19. LaTeX("4x=-y-7") → B2
  20. LaTeX("y=3x+11") → B3
  21. LaTeX("y=10x-9") → B4
  22. LaTeX("8x=5-y") → B5
  23. LaTeX("x=-4y-7") → D2
  24. LaTeX("y=-3x-11") → D3
  25. LaTeX("y=-10x+9") → D4
  26. LaTeX("8x=y-5") → D5
  27. Text(If[isLeftCorrect, correctLeftText, incorrectLeftText], puzzleAnchor + (2.75, 4), true, true) → matchedLeftText
  28. Text(If[isRightCorrect, correctRightText, incorrectRightText], puzzleAnchor + (8.15, 7), true, true) → matchedRightText
  29. LaTeX("-4x\!+\!y\!-\!7\!=\!0") → E2
  30. LaTeX("y\!-\!3x\!=\!-11") → E3
  31. LaTeX("10x\!+\!y\!+\!9\!=\!0") → E4
  32. LaTeX("y\!=\!8x\!-\!5") → E5

AI Drawing Prompt Reference

Draw a geometric illustration showing the equivalence of pairs of linear equations and their corresponding solutions. Each pair consists of a correct match and an incorrect match, distinguished by different colors. The equations are displayed as italic text on both sides of the figure, with correct matches in green and incorrect in red. Below, the corresponding analytical forms are shown, connected by arrows.
The prompt above was compiled from the original drawing commands and is for reference only.