MathPlotAI Logo MathPlotAI

Rotation Transformation and Linear Programming Demo

Rotation Transformation and Linear Programming Demo
Loading the math board and drawing, please wait…
2020-06-01 19:06
VectorTransformationOptimizationParametric EquationGeometric Construction
In collections Isometries
This example demonstrates the trajectories formed by rotating points A and B around R_(A,60) and R_(B,300) respectively, and their combined effects. Core mathematical concepts include rotation transformation, linear programming, parametric equations, and geometric construction. Key GeoGebra commands and objects used in the construction are Rotate, Line, Angle, Segment, and Vector, as outlined in the construction summary. Suitable for high school and above learners to understand the application of rotation transformations in geometric problems and the geometric meaning of linear programming.

GeoGebra Commands & Parameters

  1. Rotate(P, β, B) → P'
  2. Line(B', B) → f
  3. Angle(P, B, P') → α_1
  4. Line(A, A') → g
  5. Rotate(P', α, A) → P''
  6. Angle(P', A, P'') → β_1
  7. Rotate(g, α / 2, A) → g'
  8. Rotate(f, β / 2, B) → f'
  9. Segment(P, B) → h
  10. Segment(B, P') → i
  11. Segment(P', A) → j
  12. Segment(A, P'') → k
  13. Vector(P, P'') → u
  14. Angle(P, B, P') → γ
  15. Angle(P', A, P'') → δ