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Matrix Rotations

Matrix Rotations
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2015-10-12 22:13
TrigonometryCoordinate GeometryMatrixTransformationGeometric Construction
This example demonstrates the effects of matrix rotations on geometric figures, particularly triangles and polygons, showcasing transformations, coordinate geometry, symmetry, and rotation. It involves key math concepts like matrix transformations, geometric constructions, and symmetry. GeoGebra commands used include Intersect, Segment, Polygon, ApplyMatrix, and Angle for constructing and manipulating the figures. Suitable for high school students and above to explore the connection between linear algebra and geometric transformations, or for educational purposes.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → D
  2. Segment(D, A) → d
  3. Polygon(A, B, C) → poly1, c, a_1, b_1
  4. ApplyMatrix(M, A) → A'
  5. ApplyMatrix(M, B) → B'
  6. ApplyMatrix(M, C) → C'
  7. Polygon(A', B', C') → poly1', c', a', b'
  8. ApplyMatrix(M, D) → D'
  9. Angle(A, D, A') → α
  10. ApplyMatrix(M, D) → D'_1
  11. ApplyMatrix(M, D) → D'_2
  12. Segment(D'_2, A') → h