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Reflection in a Line by Nadezhda Konstantinova

Reflection in a Line by Nadezhda Konstantinova
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2017-01-13 23:37
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the reflection of points, line segments, and figures across a line, involving core concepts like reflection symmetry, vector operations, and coordinate geometry. It uses commands such as Point, Line, Segment, Vector, and Rotate to construct and reflect objects, making it suitable for high school mathematics instruction on geometric transformations and coordinate representation.

GeoGebra Commands & Parameters

  1. Point(yAxis) → T
  2. Line(K_1, T) → g_1
  3. Point(g_1) → U
  4. Segment(K, U) → q_1
  5. Point(q_1, (-w)) → A_1
  6. Vector(C, E) → u
  7. Vector(D, F) → v
  8. Segment(H, C) → c
  9. Ellipse((3.5, 1), (-3.5, 1), 4) → d
  10. Ellipse((0.75, 1), (-0.75, 1), 1) → e
  11. Point(d, a) → I
  12. Point(e, a) → J
  13. Ellipse((0.75, 4.64), (-0.75, 4.64), 1) → f
  14. Point(f, a) → M
  15. Ellipse((1, 0.95), (1, -0.95), 1) → h
  16. Ellipse((4, 0.95), (4, -0.95), 1) → k
  17. Point(h, i) → N
  18. Point(k, i) → O
  19. Ellipse((1, 4.5), (1, -4.5), 4.64) → p
  20. Point(p, i) → P
  21. Segment(C, N) → j
  22. Ellipse((0.95, 0.95), (-0.95, -0.95), C) → q
  23. Ellipse((3.9, 0.9), (-0.9, -3.9), D) → r
  24. Point(q, n) → Q
  25. Point(r, n) → R
  26. Ellipse((0.9, 4.6), (-4.6, -0.9), K) → s
  27. Point(s, n) → S
  28. Line(K, S) → t
  29. Line(C, Q) → a_1
  30. Line(D, R) → b_1
  31. Angle(b_1, m) → β
  32. Segment(T, C_1) → e_1
  33. Line(T, C_1) → f_1
  34. Point(f_1) → V
  35. Line(D_1, T) → h_1
  36. Segment(K_1, T) → i_1
  37. Segment(T, U) → j_1
  38. Segment(T, D_1) → l_1
  39. Point(h_1) → W
  40. Segment(T, W) → m_1
  41. Segment(V, T) → n_1
  42. Segment(W, D) → r_1
  43. Segment(V, C) → p_1
  44. Point(r_1, w) → Z
  45. Point(p_1, w) → B_1
  46. Intersect(xAxis, yAxis) → F_1
  47. Segment((0, 0), A_1) → k_1
  48. Rotate(A_1, α, (0, 0)) → E_1
  49. Segment(E_1, F_1) → s_1
  50. Textfield(α) → InputBox1
  51. Rotate(pic1, α, (0, 0)) → pic1'

AI Drawing Prompt Reference

Draw a horizontal line with a point on it, then create a line segment and its reflection across the line. Next, draw two ellipses and their reflections, along with the mirrored versions of these ellipses and the shapes formed by them. Finally, illustrate the rotational symmetry of these figures and label key points and lines.
The prompt above was compiled from the original drawing commands and is for reference only.