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Geometric Transformation of Quadrilateral

Geometric Transformation of Quadrilateral
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2019-06-20 12:07
PolygonTransformationGeometric Construction
This example demonstrates the geometric transformation of a quadrilateral, particularly similarity transformation. It shows how to construct a quadrilateral with specific properties using transformation operations like mirroring. Commands used include Polygon, PointIn, Line, Mirror, etc. Suitable for middle school and above students or teachers to understand geometric transformations and similarity.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F, G) → poly1, a, b, c, d, e, f, g
  2. Polygon(I, J, K, L, M, N, O) → poly2, ı, j, k, l, m, n, o
  3. Polygon(Q, R, S, T, U, V) → poly3, q, r, s, t, u, v
  4. Polygon(Z, A_1, B_1) → t1, b_1, z_1, a_1
  5. Polygon(D_1, E_1, F_1, G_1) → q1, d_1, e_1, f_1, g_1
  6. PointIn(q1) → Pointq1
  7. PointIn(t1) → Pointt1
  8. PointIn(poly3) → Pointpoly3
  9. PointIn(poly2) → Pointpoly2
  10. PointIn(poly1) → Pointpoly1
  11. Line(W, C_1) → h
  12. Mirror(A, h) → A'
  13. Mirror(B, h) → B'
  14. Mirror(C, h) → C'
  15. Mirror(D, h) → D'
  16. Mirror(E, h) → E'
  17. Mirror(F, h) → F'
  18. Mirror(G, h) → G'
  19. Polygon(A', B', C', D', E', F', G') → poly1', a', b', c', d', e', f', g'
  20. Mirror(I, h) → I'
  21. Mirror(J, h) → J'
  22. Mirror(K, h) → K'
  23. Mirror(L, h) → L'
  24. Mirror(M, h) → M'
  25. Mirror(N, h) → N'
  26. Mirror(O, h) → O'
  27. Polygon(I', J', K', L', M', N', O') → poly2', ı', j', k', l', m', n', o'
  28. Mirror(Q, h) → Q'
  29. Mirror(R, h) → R'
  30. Mirror(S, h) → S'
  31. Mirror(T, h) → T'
  32. Mirror(U, h) → U'
  33. Mirror(V, h) → V'
  34. Polygon(Q', R', S', T', U', V') → poly3', q', r', s', t', u', v'
  35. Mirror(Z, h) → Z'
  36. Mirror(A_1, h) → H_1
  37. Mirror(B_1, h) → I_1
  38. Polygon(Z', H_1, I_1) → t1', ı_1, z', h_1
  39. Mirror(D_1, h) → J_1
  40. Mirror(E_1, h) → K_1
  41. Mirror(F_1, h) → L_1
  42. Mirror(G_1, h) → M_1
  43. Polygon(J_1, K_1, L_1, M_1) → q1', j_1, k_1, l_1, m_1
  44. Polygon(K_1, M_1, Q', Z', F', E', M', N') → poly4, i, p, i_1, n_1, p_1, q_1, r_1, s_1

AI Drawing Prompt Reference

Draw a quadrilateral and create a similar quadrilateral through a reflection transformation to demonstrate the geometric transformation process. First, draw a quadrilateral, then use a line as a mirror to reflect the quadrilateral along this line, obtaining a new quadrilateral. Perform the same reflection operation on the second quadrilateral to observe the changes in the shape. Finally, combine all the quadrilaterals and the mirror line to clearly show the geometric relationship of the similarity transformation.
The prompt above was compiled from the original drawing commands and is for reference only.