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Matrix Representation of a Rotation

Matrix Representation of a Rotation
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2016-02-14 00:05
VectorCoordinate GeometryMatrixTransformationGeometric Construction
This example demonstrates how a rotation matrix is represented using points A and B to control its columns. It shows how a rotation operation can be expressed through vectors. Commands used include Sequence, Point, Segment, Vector, Polygon, and ApplyMatrix. Suitable for high school mathematics, particularly in coordinate geometry and transformations.

GeoGebra Commands & Parameters

  1. Sequence((cos(t), sin(t)), t, 0*°, 350*°, 10*°) → pts
  2. Point(pts) → A
  3. Segment((0, 0), A) → a
  4. Vector((0, 0), A) → u
  5. Vector((0, 0), B) → v
  6. Polygon(C, D, E, F, G, H, I, J, K, L) → poly1, c, l, d, e, f, g, h, i, j, k
  7. ApplyMatrix(matrix1, C) → C'
  8. ApplyMatrix(matrix1, D) → D'
  9. ApplyMatrix(matrix1, E) → E'
  10. ApplyMatrix(matrix1, F) → F'
  11. ApplyMatrix(matrix1, G) → G'
  12. ApplyMatrix(matrix1, H) → H'
  13. ApplyMatrix(matrix1, I) → I'
  14. ApplyMatrix(matrix1, J) → J'
  15. ApplyMatrix(matrix1, K) → K'
  16. ApplyMatrix(matrix1, L) → L'
  17. Polygon(C', D', E', F', G', H', I', J', K', L') → poly1', c', l', d', e', f', g', h', i', j', k'
  18. Sequence(Line[(t * B), u], t, -20, 20) → list1
  19. Sequence(Line[(t * A), v], t, -20, 20) → list2