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Double Reflection Over Parallel Lines by Matt James

Double Reflection Over Parallel Lines by Matt James
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2015-02-10 11:10
VectorCoordinate GeometryGeometric Construction
This example demonstrates the trajectory transformation of a point or shape undergoing two reflections over parallel lines. Key mathematical concepts include reflection transformation, translation, vector operations, and coordinate geometry. The construction utilizes GeoGebra commands and objects such as Polygon, Line, Mirror, OrthogonalLine, Intersect, Segment, Point, and Midpoint as outlined in the construction summary. Suitable for high school and above learners to explore transformation geometry and vector applications in plane 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. Polygon(M, N, O, P, Q) → poly1', r, s, t, a_1, b_1
  17. OrthogonalLine(F, g) → k
  18. Intersect(g, k) → K
  19. Segment(F, K) → l
  20. Segment(D, D'') → m
  21. Segment(F, G) → p
  22. Point(g) → L
  23. Segment(H, L) → q
  24. Midpoint(N, P) → I
  25. Midpoint(P, O) → J
  26. Line(O, I) → c_1
  27. Line(N, J) → d_1
  28. Intersect(c_1, d_1) → R