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Symmetry Transformation and Vectors

Symmetry Transformation and Vectors
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2014-08-07 22:15
VectorTransformationGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates the basic concepts of symmetry transformation and vectors. Using GeoGebra commands such as Mirror and Translate, it visually illustrates vector addition and subtraction, as well as the effects of symmetry transformations. Suitable for students at junior high school level and above to learn about geometric transformations and vector operations.

GeoGebra Commands & Parameters

  1. Segment(K, N) → h
  2. Segment(K, M) → g
  3. Segment(K, L) → f
  4. Segment(J, K) → e
  5. Midpoint(C, A) → H
  6. Point(xAxis) → B
  7. Midpoint(C, B) → I
  8. Vector(C, I) → t
  9. Vector(B, I) → w
  10. Midpoint(D, C) → G
  11. Midpoint(B, D) → F
  12. Segment(H, F) → b
  13. Mirror(cell1, b) → cell3
  14. Translate(cell3, t) → cell3a
  15. Midpoint(A, B) → E
  16. Segment(E, G) → c
  17. Mirror(cell1, c) → cell2
  18. Translate(cell2, w) → cell2a
  19. Mirror(cell2, b) → cell4
  20. Vector(A, B) → u
  21. Vector(A, C) → v
  22. Vector(C, D) → w_1
  23. Vector(B, D) → a
  24. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  25. Segment(H, I) → r
  26. Segment(E, I) → s
  27. LineBisector(C, G) → k
  28. LineBisector(G, D) → l
  29. LineBisector(C, H) → m
  30. LineBisector(H, A) → n

AI Drawing Prompt Reference

Draw a geometric figure involving vectors and symmetry transformations. Start by drawing vectors u, v, and w_1, then points A, B, C, D, and K. Draw segments g, h, f, e, b, c, r, and s. Use symmetry transformations and vector translations to create mirrored and moved versions of the figure. Finally, draw segments k, l, m, and n to demonstrate the effects of geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.