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Images of F under Matrix Transformations

Images of F under Matrix Transformations
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2019-07-28 23:07
MatrixTransformationGeometric Construction
This example demonstrates the images of a figure under matrix transformations. Key mathematical concepts include matrix transformations, similarity transformations, and geometric transformations. Using commands like Intersect, Vector, Polygon, ApplyMatrix, Line, and Sequence, a series of transformed figures can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. Vector(A, C) → v
  4. Polygon(D, E, F, G, H, I, J, K, L, M) → poly1, d, m, e, f, g, h, i, j, k, l
  5. ApplyMatrix(m1, D) → D'
  6. ApplyMatrix(m1, E) → E'
  7. ApplyMatrix(m1, F) → F'
  8. ApplyMatrix(m1, G) → G'
  9. ApplyMatrix(m1, H) → H'
  10. ApplyMatrix(m1, I) → I'
  11. ApplyMatrix(m1, J) → J'
  12. ApplyMatrix(m1, K) → K'
  13. ApplyMatrix(m1, L) → L'
  14. ApplyMatrix(m1, M) → M'
  15. Polygon(D', E', F', G', H', I', J', K', L', M') → poly1', d', m', e', f', g', h', i', j', k', l'
  16. Line(A, B) → n
  17. Line(A, C) → p
  18. Sequence((w * B), w, -10, 10) → l1
  19. Sequence((w * C), w, -10, 10) → l2
  20. Sequence(Line[(w * C), u], w, -20, 20) → l3
  21. Sequence(Line[(w * B), v], w, -20, 20) → l4
  22. Sequence(Line[(0, w), xAxis], w, -20, 20) → l5
  23. Sequence(Line[(w, 0), yAxis], w, -20, 20) → l6