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Reflection across two parallel lines

Reflection across two parallel lines
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2016-02-29 02:26
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the reflection transformation of points, polygons, and other figures across two parallel lines. It involves core mathematical concepts such as reflection symmetry, properties of parallel lines, and coordinate geometry. The construction utilizes GeoGebra commands and objects like Line, Polygon, Mirror, Point, OrthogonalLine, Intersect, and Segment. Suitable for high school students learning geometric transformations and analytical geometry.

GeoGebra Commands & Parameters

  1. Line(D, E) → a
  2. Line(F, a) → b
  3. Polygon(B, A, C) → poly1, f, d, e
  4. Mirror(B, a) → B'
  5. Mirror(A, a) → A'
  6. Mirror(C, a) → C'
  7. Polygon(B', A', C') → poly1', c', b', a'
  8. Mirror(B', b) → B''
  9. Mirror(A', b) → A''
  10. Mirror(C', b) → C''
  11. Polygon(B'', A'', C'') → poly1'', c'', b'', a''
  12. Point(b) → D_1
  13. OrthogonalLine(D_1, a) → h
  14. Intersect(h, a) → E_1
  15. Segment(E_1, D_1) → i
  16. Segment(C, C'') → j
  17. Segment(A, A'') → k
  18. Segment(B, B'') → l