MathPlotAI Logo MathPlotAI

Graphical Solution of a Linear System

Graphical Solution of a Linear System
Loading the math board and drawing, please wait…
2019-04-10 23:57
Coordinate GeometryGeometric Construction
This example demonstrates solving a linear system graphically. Key mathematical concepts include the graphical representation of linear systems and their intersections. GeoGebra commands used include Point, Element, Polygon, Line, Intersect, etc. Suitable for students in middle school and above studying linear algebra and coordinate geometry.

GeoGebra Commands & Parameters

  1. Point({userPOIx, userPOIy}) → userPOI
  2. Element(questionList, questionListIndex) → questionNum
  3. Element(C2:C5, questionNum) → poi
  4. Polygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → viewBox
  5. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  6. DynamicCoordinates(free1A, If[IsInRegion[free1A, viewBox], x(free1A), 18.5], If[IsInRegion[free1A, viewBox], y(free1A), 7.25]) → line1A
  7. DynamicCoordinates(free2A, If[IsInRegion[free2A, viewBox], x(free2A), 18.5], If[IsInRegion[free2A, viewBox], y(free2A), 1.25]) → line2A
  8. DynamicCoordinates(free2B, If[IsInRegion[free2B, viewBox], x(free2B), 20.5], If[IsInRegion[free2B, viewBox], y(free2B), 1.25]) → line2B
  9. DynamicCoordinates(free1B, If[IsInRegion[free1B, viewBox], x(free1B), 20.5], If[IsInRegion[free1B, viewBox], y(free1B), 7.25]) → line1B
  10. Line(line1A, line1B) → userLine1
  11. Line(line2A, line2B) → userLine2
  12. Intersect(A2, B2) → C2
  13. Intersect(A3, B3) → C3
  14. Intersect(A4, B4) → C4
  15. Intersect(A5, B5) → C5
  16. Element(A2:A5, questionNum) → line1
  17. Element(B2:B5, questionNum) → line2
  18. LaTeX(("\text{Line 1: }" * line1)) → labelLine1
  19. LaTeX(("\text{Line 2: }" * line2)) → labelLine2
  20. LaTeX("\text{Points: }") → pointsLine1
  21. LaTeX("\text{Points: }") → pointsLine2
  22. Textfield(textPOIx) → ansBoxX
  23. Textfield(textPOIy) → ansBoxY
  24. LaTeX("\begin{tabular}{c}\text{The solution is}\\(\hspace{45},\hspace{45})\end{tabular}") → solution
  25. LaTeX(activePoint) → activePointLabel
  26. LaTeX(poi) → poiLabel
  27. LaTeX("\text{Line 1}") → line1LabelOnGrid
  28. LaTeX("\text{Line 2}") → line2LabelOnGrid

AI Drawing Prompt Reference

Draw two lines within a coordinate grid and mark their intersection point. First, create a bounding box within the coordinate system, then draw two lines that can be dynamically adjusted to stay inside the box. Next, find the intersection point of the two lines and highlight it with a distinct color or marker. Finally, add text labels to indicate the equations of the lines and the coordinates of the intersection point.
The prompt above was compiled from the original drawing commands and is for reference only.