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Transformations of Parallel Line Segments

Transformations of Parallel Line Segments
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2017-11-11 05:51
VectorTransformationGeometric Construction
This example demonstrates the changes in parallel line segments under transformations such as mirroring, rotation, translation, and dilation. Key mathematical concepts include line segment transformations, vectors, and ratios. Using GeoGebra commands like Segment, Point, Line, Mirror, Rotate, Translate, and Dilate, the transformations are visually illustrated. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(C, D) → g
  3. Point(f) → E
  4. Line(F, G) → h
  5. Mirror(A, h) → A'
  6. Mirror(B, h) → B'
  7. Segment(A', B') → f'
  8. Mirror(C, h) → C'
  9. Mirror(D, h) → D'
  10. Segment(C', D') → g'
  11. Mirror(E, h) → E'
  12. Rotate(A, 180°, F) → A'_1
  13. Rotate(B, 180°, F) → B'_1
  14. Segment(A'_1, B'_1) → f'_1
  15. Rotate(C, 180°, F) → C'_1
  16. Rotate(D, 180°, F) → D'_1
  17. Segment(C'_1, D'_1) → g'_1
  18. Rotate(E, 180°, F) → E'_1
  19. Vector(H, I) → u
  20. Translate(A, u) → A'_2
  21. Translate(B, u) → B'_2
  22. Segment(A'_2, B'_2) → f'_2
  23. Translate(C, u) → C'_2
  24. Translate(D, u) → D'_2
  25. Segment(C'_2, D'_2) → g'_2
  26. Translate(E, u) → E'_2
  27. Dilate(A, 2, J) → A'_3
  28. Dilate(B, 2, J) → B'_3
  29. Segment(A'_3, B'_3) → f'_3
  30. Dilate(C, 2, J) → C'_3
  31. Dilate(D, 2, J) → D'_3
  32. Segment(C'_3, D'_3) → g'_3
  33. Dilate(E, 2, J) → E'_3