MathPlotAI Logo MathPlotAI

Transformations of Shapes: Rotation, Reflection, Translation, Enlargement

Transformations of Shapes: Rotation, Reflection, Translation, Enlargement
Loading the math board and drawing, please wait…
2015-01-27 02:04
VectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates transformations of basic geometric shapes including rotation, reflection, translation, and enlargement. It involves core math concepts like geometric transformations, vectors, and coordinate geometry. Constructed using commands like Polygon, Line, Mirror, Dilate, Rotate, Vector, Translate, Ray, and objects A, B, C, etc. Ideal for middle school and above students to learn properties and applications of geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, E, C) → poly1, a, b, d, e, c
  2. Line(G, H) → f
  3. Mirror(A, f) → A'
  4. Mirror(B, f) → B'
  5. Mirror(D, f) → D'
  6. Mirror(E, f) → E'
  7. Mirror(C, f) → C'
  8. Polygon(A', B', D', E', C') → poly1', a', b', d', e', c'
  9. Dilate(A, g, F) → A'_1
  10. Dilate(B, g, F) → B'_1
  11. Dilate(D, g, F) → D'_1
  12. Dilate(C, g, F) → C'_1
  13. Rotate(A, (-α), F) → A'_2
  14. Rotate(B, (-α), F) → B'_2
  15. Rotate(D, (-α), F) → D'_2
  16. Rotate(E, (-α), F) → E'_2
  17. Rotate(C, (-α), F) → C'_2
  18. Polygon(A'_2, B'_2, D'_2, E'_2, C'_2) → poly1'_2, a'_2, b'_2, d'_2, e'_2, c'_2
  19. Dilate(A, g, F) → A'_3
  20. Dilate(B, g, F) → B'_3
  21. Dilate(D, g, F) → D'_3
  22. Dilate(E, g, F) → E'_1
  23. Dilate(C, g, F) → C'_3
  24. Polygon(A'_3, B'_3, D'_3, E'_1, C'_3) → poly1'_1, a'_3, b'_3, d'_3, e'_1, c'_3
  25. Vector(F, I) → u
  26. Translate(A, u) → A'_4
  27. Translate(B, u) → B'_4
  28. Translate(D, u) → D'_4
  29. Translate(E, u) → E'_3
  30. Translate(C, u) → C'_4
  31. Polygon(A'_4, B'_4, D'_4, E'_3, C'_4) → poly1'_3, a'_4, b'_4, d'_4, e'_3, c'_4
  32. Ray(F, B) → l
  33. Ray(F, D) → m
  34. Ray(F, A) → n
  35. Ray(F, E) → p
  36. Ray(F, C) → q