MathPlotAI Logo MathPlotAI

Investigate Two Rotations

Investigate Two Rotations
Loading the math board and drawing, please wait…
2014-08-05 19:29
TriangleCoordinate GeometryTransformation
This example demonstrates the combined effect of two rotations. It involves the concepts of similar triangles and rotation. Using GeoGebra commands such as Polygon, Rotate, Line, Intersect, and Mirror, the construction of the rotated figures is shown. Suitable for middle or high school geometry education, helping students understand the transformation of rotation and its combination effects.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d
  2. Rotate(A, α, O) → A'
  3. Rotate(B, α, O) → B'
  4. Rotate(C, α, O) → C'
  5. Rotate(D, α, O) → D'
  6. Polygon(A', B', C', D') → poly1', a', b', c', d'
  7. Rotate(A', β, Q) → A''
  8. Rotate(B', β, Q) → B''
  9. Rotate(C', β, Q) → C''
  10. Rotate(D', β, Q) → D''
  11. Polygon(A'', B'', C'', D'') → poly1'', a'', b'', c'', d''
  12. Line(Q, O) → a
  13. Rotate(a, ((-α)) / 2, O) → b
  14. Rotate(a, β / 2, Q) → c
  15. Intersect(c, b) → R
  16. Mirror(A, b) → A'_1
  17. Mirror(B, b) → B'_1
  18. Mirror(C, b) → C'_1
  19. Mirror(D, b) → D'_1
  20. Polygon(A'_1, B'_1, C'_1, D'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1