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Double Reflection Over Parallel Lines

Double Reflection Over Parallel Lines
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2017-03-07 23:38
Coordinate GeometryGeometric Construction
This example demonstrates the geometric transformation phenomenon of a point undergoing double reflection over parallel lines. It involves core mathematical concepts such as reflection transformations, properties of parallel lines, and geometric constructions. The construction utilizes GeoGebra commands/objects like Polygon, Line, Mirror, OrthogonalLine, Intersect, Segment, Point, and Midpoint. It is suitable for high school students studying geometric transformations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  2. Line(F, G) → f
  3. Line(H, f) → g
  4. Mirror(A, f) → A'_1
  5. Mirror(B, f) → B'_1
  6. Mirror(C, f) → C'_1
  7. Mirror(D, f) → D'_1
  8. Mirror(E, f) → E'_1
  9. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1) → poly1'_1, a', b', c', d', e'
  10. Mirror(A'_1, g) → A''
  11. Mirror(B'_1, g) → B''
  12. Mirror(C'_1, g) → C''
  13. Mirror(D'_1, g) → D''
  14. Mirror(E'_1, g) → E''
  15. Polygon(A'', B'', C'', D'', E'') → poly1'', a'', b'', c'', d'', e''
  16. OrthogonalLine(F, g) → k
  17. Intersect(g, k) → K
  18. Segment(F, K) → l
  19. Segment(D, D'') → m
  20. Segment(F, G) → p
  21. Point(g) → L
  22. Segment(H, L) → q
  23. Midpoint(N, P) → I
  24. Midpoint(P, O) → J
  25. Line(O, I) → c_1
  26. Line(N, J) → d_1
  27. Intersect(c_1, d_1) → R