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Reflection over Intersecting Lines

Reflection over Intersecting Lines
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2016-07-12 04:10
VectorTransformationGeometric Construction
This example demonstrates the reflection of points and polygons over two intersecting lines, involving core concepts like reflection, rotation, median line, vectors, and trigonometric functions. It uses commands such as Line, Point, Polygon, Mirror, Segment, Distance, Intersect, Angle, Circle, and CircleSector for construction, suitable for high school mathematics education to explore the properties and calculations of reflection transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → R1
  2. Point(Circle[C, 5.548885023137532]) → D
  3. Polygon(C, D, E, F, G, H, I, J) → poly1, c, d, e, f, g, h, i, j
  4. Mirror(C, R1) → C'
  5. Mirror(D, R1) → D'
  6. Mirror(E, R1) → E'
  7. Mirror(F, R1) → F'
  8. Mirror(G, R1) → G'
  9. Mirror(H, R1) → H'
  10. Mirror(I, R1) → I'
  11. Mirror(J, R1) → J'
  12. Polygon(C', D', E', F', G', H', I', J') → poly1', c', d', e', f', g', h', i', j'
  13. Segment(C, C') → l
  14. Segment(D, D') → m
  15. Distance(C, C') → distanceCC'
  16. Distance(E, E') → distanceEE'
  17. Distance(F, F') → distanceFF'
  18. Line(K, L) → k
  19. Mirror(C', k) → C''
  20. Mirror(D', k) → D''
  21. Mirror(E', k) → E''
  22. Mirror(F', k) → F''
  23. Mirror(G', k) → G''
  24. Mirror(H', k) → H''
  25. Mirror(I', k) → I''
  26. Mirror(J', k) → J''
  27. Polygon(C'', D'', E'', F'', G'', H'', I'', J'') → poly1'', c'', d'', e'', f'', g'', h'', i'', j''
  28. Intersect(R1, k) → M
  29. Angle(A, M, L) → α
  30. Angle(C, M, C'') → β
  31. Segment(C, M) → p
  32. Segment(C'', M) → q
  33. Angle(J, M, J'') → γ
  34. Angle(I, M, I'') → δ
  35. Point(p) → N
  36. Circle(M, N) → r
  37. Intersect(r, q, 1) → O
  38. CircleSector(M, N, O) → t
  39. Angle(H, M, H'') → ε
  40. Angle(G, M, G'') → ζ
  41. Angle(F, M, F'') → η
  42. Angle(E, M, E'') → θ
  43. Angle(D, M, D'') → ι

AI Drawing Prompt Reference

Draw a polygon with vertices C, D, E, F, G, H, I, J and its reflections over two intersecting lines R1 and k. First, draw the two intersecting lines R1 and k, then reflect each vertex of the polygon over these lines to get the reflected polygon. Next, connect the original points to their reflections, calculate the distances, and construct circles and sectors. Finally, label the angles.
The prompt above was compiled from the original drawing commands and is for reference only.