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System of Three Equations by Matthew Watts

System of Three Equations by Matthew Watts
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2015-06-19 05:38
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric representation of a system of three equations, showing the intersection point of three planes as the solution. Core math concepts include spatial geometry, linear equation systems, polygon and prism constructions. It uses commands like PointIn, Line, Polygon, Prism from GeoGebra. Suitable for high school and above students studying spatial analytical geometry, linear algebra, and geometric intuition.

GeoGebra Commands & Parameters

  1. PointIn(P2) → A
  2. PointIn(P1) → B
  3. Line(A, B) → a
  4. PointIn(P2) → J
  5. Polygon(A, C, E, D) → poly1, a_1, c, e, d
  6. Polygon(E, F, I, G) → poly2, e_1, f, i, g
  7. PointIn(P2) → K
  8. Prism(poly2, H) → b, L, edgeFL, edgeIM, edgeGN, edgeHL, edgeLM, edgeMN, edgeHN, M, N, faceEFLH, faceFIML, faceGIMN, faceEGNH, faceHLMN, edgeEH

AI Drawing Prompt Reference

Draw the intersection point of three planes in 3D space. Construct a quadrilateral with points A, B, C, and D, then another quadrilateral with points E, F, G, and H. Finally, use points I, J, K, and H to form a pentahedron. Pay attention to the intersection point of the three planes, which is the common point of the quadrilaterals and pentahedron.
The prompt above was compiled from the original drawing commands and is for reference only.