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Symmetry and Matrix Transformations Demo

Symmetry and Matrix Transformations Demo
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2014-08-04 13:05
PolygonVectorMatrixGeometric Construction
This example dynamically demonstrates symmetry in plane figures and matrix transformations, involving core concepts like symmetry, plane shapes, median value, line segments, matrices, difference, and slope. It uses GeoGebra commands like Point, Midpoint, Vector, Segment, Mirror, Sequence, and Line. Suitable for high school mathematics teaching on geometric transformations and matrix applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Midpoint(A, B) → E
  3. Midpoint(B, D) → F
  4. Midpoint(D, C) → G
  5. Midpoint(C, A) → H
  6. Midpoint(C, B) → I
  7. Vector(A, B) → u
  8. Vector(A, C) → v
  9. Vector(C, D) → w
  10. Vector(B, D) → a
  11. Segment(H, F) → b
  12. Segment(E, G) → c
  13. Segment(J, K) → e
  14. Segment(K, L) → f
  15. Segment(K, M) → g
  16. Segment(K, N) → h
  17. Mirror(cell1, c) → cell2
  18. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  19. Line(C, A) → k
  20. Line(G, E) → l
  21. Line(D, B) → m

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, find its diagonal intersection points E, F, G, H, and the midpoints I of sides AB, BC, CD, DA. Then draw vectors u, v, w, a, and line segments EF, GH, IJ, JK, KL, KM, KN. Use line segment IJ as the mirror to reflect line segment GH. Finally, translate and rotate quadrilateral ABCD to form the transformed pattern.
The prompt above was compiled from the original drawing commands and is for reference only.