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Basic Matrix Transformations

Basic Matrix Transformations
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2016-06-22 08:18
Coordinate GeometryMatrixGeometric Construction
This example demonstrates basic geometric transformations using a 2x2 matrix. It involves core math concepts like reflection, rotation, shearing, and scaling. Construction highlights include using GeoGebra commands and objects such as Element, SelectedIndex, Intersect, Circle, OrthogonalLine, Polygon, Point, Vector, Determinant, ApplyMatrix, Flatten, and Textfield. Suitable for high school and above, for understanding matrix transformations in plane geometry applications.

GeoGebra Commands & Parameters

  1. Element(Reflections, (2 * indexreflection) - 1) → reflectiony1
  2. Element(Reflections, (2 * indexreflection)) → reflectiony2
  3. SelectedIndex(Listnames) → Indexnames
  4. Intersect(xAxis, yAxis) → A
  5. Circle(A, 1) → unitcircle
  6. Intersect(unitcircle, xAxis, 1) → B
  7. OrthogonalLine(B, xAxis) → f
  8. Intersect(unitcircle, yAxis, 2) → C
  9. OrthogonalLine(C, yAxis) → g
  10. Intersect(unitcircle, yAxis, 1) → D
  11. Intersect(unitcircle, xAxis, 2) → E
  12. OrthogonalLine(E, xAxis) → h
  13. OrthogonalLine(D, f) → i
  14. Intersect(f, g) → F
  15. Intersect(g, h) → G
  16. Intersect(h, i) → H
  17. Intersect(f, i) → I
  18. Polygon(I, H, G, F) → poly1, i_1, h_1, g_1, f_1
  19. Point(poly1) → P
  20. Element(ListMatrix, Indexnames) → T
  21. Vector((0, 0), P') → u
  22. Vector(TP) → Tu
  23. Determinant(T) → det
  24. ApplyMatrix(Tanimated, I) → I'
  25. ApplyMatrix(Tanimated, H) → H'
  26. ApplyMatrix(Tanimated, G) → G'
  27. ApplyMatrix(Tanimated, F) → F'
  28. Polygon(I', H', G', F') → poly1', i'_1, h'_1, g'_1, f'_1
  29. ApplyMatrix(Tanimated, pic1) → pic1'
  30. ApplyMatrix(T, pic1) → pic1'_1
  31. Element(ListMatrixtext, Indexnames) → Ttext
  32. Flatten(T) → list1
  33. ApplyMatrix(T, I) → I'_1
  34. ApplyMatrix(T, H) → H'_1
  35. ApplyMatrix(T, G) → G'_1
  36. ApplyMatrix(T, F) → F'_1
  37. Polygon(I'_1, H'_1, G'_1, F'_1) → poly1'_1, i'_2, h'_2, g'_2, f'_2
  38. Element(list1, 1) → a
  39. Element(list1, 2) → b
  40. Element(list1, 3) → c
  41. Element(list1, 4) → d
  42. Textfield(scaling) → InputBox1
  43. Textfield(k) → InputBox2
  44. Textfield(θ) → InputBox3
  45. Textfield(m) → InputBox4