Tess 5

Tess 5
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2013-04-10 01:40
This example demonstrates the translation of polygons. Key mathematical concepts include polygons, vectors, and translation. Using commands like Polygon, Segment, Vector, and Translate, the construction of translated polygons is shown. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Segment(C, E) → e
  3. Segment(E, F) → f
  4. Segment(F, G) → g
  5. Segment(G, H) → h
  6. Segment(H, I) → i
  7. Segment(I, J) → j
  8. Segment(J, B) → k
  9. Vector(C, D) → u
  10. Translate(B, u) → B'
  11. Translate(C, u) → C'
  12. Segment(B', C') → b'
  13. Translate(C, u) → C'_1
  14. Translate(E, u) → E'
  15. Segment(C'_1, E') → e'
  16. Translate(E, u) → E'_1
  17. Translate(F, u) → F'
  18. Segment(E'_1, F') → f'
  19. Translate(F, u) → F'_1
  20. Translate(G, u) → G'
  21. Segment(F'_1, G') → g'
  22. Translate(G, u) → G'_1
  23. Translate(H, u) → H'
  24. Segment(G'_1, H') → h'
  25. Translate(H, u) → H'_1
  26. Translate(I, u) → I'
  27. Segment(H'_1, I') → i'
  28. Translate(I, u) → I'_1
  29. Translate(J, u) → J'
  30. Segment(I'_1, J') → j'
  31. Translate(J, u) → J'_1
  32. Translate(B, u) → B'_1
  33. Segment(J'_1, B'_1) → k'
  34. Segment(D, K) → l
  35. Segment(K, L) → m
  36. Segment(L, M) → n
  37. Segment(M, N) → p
  38. Segment(N, O) → q
  39. Segment(O, P) → r
  40. Segment(P, Q) → s
  41. Segment(Q, R) → t
  42. Segment(R, C) → a_1
  43. Vector(D, A) → v
  44. Translate(C, v) → C'_2
  45. Translate(D, v) → D'
  46. Translate(D, v) → D'_1
  47. Translate(C, v) → C'_3
  48. Translate(u, v) → u'
  49. Translate(C', v) → C''
  50. Translate(C'_1, v) → S
  51. Vector(D, A) → w
  52. Translate(C, w) → C'_4
  53. Translate(D, w) → D'_2
  54. Segment(C'_4, D'_2) → c'_1
  55. Translate(D, w) → D'_3
  56. Translate(K, w) → K'
  57. Segment(D'_3, K') → l'
  58. Translate(K, w) → K'_1
  59. Translate(L, w) → L'
  60. Segment(K'_1, L') → m'
  61. Translate(L, w) → L'_1
  62. Translate(M, w) → M'
  63. Segment(L'_1, M') → n'
  64. Translate(M, w) → M'_1
  65. Translate(N, w) → N'
  66. Segment(M'_1, N') → p'
  67. Translate(N, w) → N'_1
  68. Translate(O, w) → O'
  69. Segment(N'_1, O') → q'
  70. Translate(O, w) → O'_1
  71. Translate(P, w) → P'
  72. Segment(O'_1, P') → r'
  73. Translate(P, w) → P'_1
  74. Translate(Q, w) → Q'
  75. Segment(P'_1, Q') → s'
  76. Translate(Q, w) → Q'_1
  77. Translate(R, w) → R'
  78. Segment(Q'_1, R') → t'
  79. Translate(R, w) → R'_1
  80. Translate(C, w) → C'_5
  81. Segment(R'_1, C'_5) → b_1
  82. Translate(u, w) → u'_1
  83. Translate(u', w) → u''
  84. Translate(C', w) → C''_1
  85. Translate(C'_1, w) → T
  86. Polygon(I', O', N', M', L', K', A, J') → poly2, i'_1, o', n'_1, m'_1, l'_1, k'_1, a_2, j'_1
  87. Polygon(R', Q', G, H, I, J, B) → poly3, r'_1, q'_1, g_1, h_1, i_1, j_1, b_2
  88. Polygon(O, P, N) → poly4, n_1, o, p_1
  89. Segment(P, U) → c_1
  90. Segment(U, V) → d_1
  91. Segment(V, W) → e_1
  92. Segment(W, Z) → f_1
  93. Segment(Z, C) → k_1
  94. Segment(Z, A_1) → l_1
  95. Segment(A_1, B_1) → m_1
  96. Segment(B_1, C_1) → q_1
  97. Segment(C_1, G) → r_1
  98. Segment(M, D_1) → s_1
  99. Segment(D_1, E_1) → t_1
  100. Segment(E_1, F_1) → c_2
  101. Segment(F_1, Z) → d_2
  102. Segment(M, G_1) → e_2
  103. Segment(G_1, H_1) → f_2
  104. Segment(H_1, F') → g_2
  105. Segment(F', I_1) → h_2
  106. Segment(I_1, J_1) → i_2
  107. Segment(J_1, I') → j_2
  108. Polygon(D, K, L, M, G_1, H_1, F', E') → poly5, d_3, k_2, l_2, m_2, g_3, h_3, f'_1, e'_1
  109. Polygon(M, D_1, P', O', I', J_1, I_1, F', H_1, G_1, E_1, F_1, Z, A_1, B_1, C_1, G, Q') → poly6, m_3, q'_2, p'_1, o'_1, i'_2, j_3, i_3, f'_2, h_4, g_5, d_4, e_3, f_3, z, a_3, b_3, c_3, g_4
  110. Polygon(M, D_1, E_1, F_1, Z, W, V, U, P, N) → poly7, m_4, n_2, d_5, e_4, f_4, z_1, w_1, v_1, u_1, p_2
  111. Polygon(C, Z, W, V, U, P, Q, R) → poly8, c_4, z_2, w_2, v_2, u_2, p_3, q_2, r_2
  112. Polygon(Z, C, E, F, G, C_1, B_1, A_1) → poly9, z_3, c_5, e_5, f_5, g_6, c_6, b_4, a_4
  113. Polygon(F', I_1, J_1, I', H', G') → poly10, f'_3, i_4, j_4, i'_3, h'_1, g'_1

AI Drawing Prompt Reference

Draw a pentagon ABCDE, then translate it using vector u to get a new pentagon A'B'C'D'E'. Next, draw vector u from point C to point D, and translate points C and D using vector u and v to get points C'2 and D'. Finally, draw vector v from point D' to point A, and translate point D' using vector v to get point D'_1.
The prompt above was compiled from the original drawing commands and is for reference only.