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Multi-Step Transformations Demo

Multi-Step Transformations Demo
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2014-06-14 12:12
VectorCoordinate GeometryTransformationGeometric Construction
In collections Transformations Stations
This example demonstrates interactive single or multi-step transformations. Users can control the transformation process using sliders and interactive elements, visually showcasing the effects of geometric transformations. Core math concepts include geometric transformations, similarity, symmetry, and coordinate geometry. Construction highlights the use of GeoGebra commands such as Line, Mirror, Dilate, Polygon, Vector, Rotate, Angle, Segment, and Translate. Suitable for high school students learning geometric transformations and spatial geometry.

GeoGebra Commands & Parameters

  1. Line(D, E) → Mirror_1
  2. Mirror(B, Mirror_1) → B'_3
  3. Dilate(T, T_2 / 100, B'_3) → T'
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Dilate(F, T_1 / 100, B) → F'
  6. Vector(B, F') → u
  7. Rotate(A, ((T_1 / 100 * 360))°, G) → A'
  8. Rotate(B, ((T_1 / 100 * 360))°, G) → B'
  9. Rotate(C, ((T_1 / 100 * 360))°, G) → C'
  10. Polygon(A', B', C') → poly1', c', a', b'
  11. Angle(B, G, B') → α
  12. Dilate(B, 0.2, G) → B'_1
  13. Dilate(B', 0.2, G) → B''
  14. Segment(G, B'_1) → d
  15. Segment(G, B'') → e
  16. Translate(A, u) → A'_1
  17. Translate(B, u) → B'_2
  18. Translate(C, u) → C'_1
  19. Polygon(A'_1, B'_2, C'_1) → poly1'_1, c'_1, a'_1, b'_2
  20. Mirror(A, Mirror_1) → A'_2
  21. Mirror(C, Mirror_1) → C'_2
  22. Dilate(A'_2, T_1 / 100, A) → H
  23. Dilate(B'_3, T_1 / 100, B) → I
  24. Dilate(C'_2, T_1 / 100, C) → J
  25. Polygon(J, H, I) → poly2, i, j, h
  26. Rotate(A'_1, ((T_2 / 100 * 360))°, K) → L
  27. Rotate(If[Translate_1, B'_2, I], ((T_2 / 100 * 360))°, K) → M
  28. Rotate(C'_1, ((T_2 / 100 * 360))°, K) → N
  29. Polygon(L, M, N) → poly3, n, l, m
  30. Dilate(M, 0.2, K) → M'
  31. Dilate(If[Translate_1, F, I], 0.2, K) → F'_1
  32. Segment(K, M') → f
  33. Segment(K, F'_1) → g
  34. Angle(F'_1, K, M') → β
  35. Line(O, P) → k
  36. Mirror(F, k) → F'_2
  37. Mirror(C'_1, k) → Q
  38. Mirror(A'_1, k) → R
  39. Dilate(Q, T_2 / 100, C'_1) → Q'
  40. Dilate(F'_2, T_2 / 100, F) → S
  41. Dilate(R, T_2 / 100, A'_1) → R'
  42. Polygon(Q', S, R') → poly4, r', q', s
  43. Vector(B'_3, T') → v
  44. Translate(A'_2, v) → A''
  45. Translate(B'_3, v) → B''_1
  46. Translate(C'_2, v) → C''
  47. Polygon(A'', B''_1, C'') → poly1'', c'', a'', b''_1
  48. Mirror(B', k) → B''_2
  49. Mirror(C', k) → C''_1
  50. Mirror(A', k) → A''_1
  51. Dilate(B''_2, T_2 / 100, B') → U
  52. Dilate(A''_1, T_2 / 100, A') → V
  53. Dilate(C''_1, T_2 / 100, C') → W
  54. Polygon(U, W, V) → poly5, v_1, u_1, w
  55. Dilate(T, T_2 / 100, B') → T'_1
  56. Vector(B', T'_1) → p
  57. Translate(A', p) → A''_2
  58. Translate(B', p) → B''_3
  59. Translate(C', p) → C''_2
  60. Polygon(A''_2, B''_3, C''_2) → poly1''_1, c''_2, a''_2, b''_3
  61. Rotate(J, β, K) → J'
  62. Rotate(H, β, K) → H'
  63. Rotate(I, β, K) → I'
  64. Polygon(J', H', I') → poly2', i', j', h'
  65. Mirror(B'_3, k) → Z
  66. Mirror(A'_2, k) → A_1
  67. Mirror(C'_2, k) → B_1
  68. Dilate(Z, T_2 / 100, B'_3) → Z'
  69. Dilate(A_1, T_2 / 100, A'_2) → C_1
  70. Dilate(B_1, T_2 / 100, C'_2) → D_1
  71. Polygon(Z', C_1, D_1) → poly6, d_1, z', c_1
  72. Dilate(A, Factor, E_1) → A'_3
  73. Dilate(B, Factor, E_1) → B'_4
  74. Dilate(C, Factor, E_1) → C'_3
  75. Polygon(A'_3, B'_4, C'_3) → poly1'_2, c'_3, a'_3, b'_4
  76. Dilate(A'_1, Factor, E_1) → F_1
  77. Dilate(B'_2, Factor, E_1) → G_1
  78. Dilate(C'_1, Factor, E_1) → H_1
  79. Polygon(F_1, G_1, H_1) → poly7, h_1, f_1, g_1
  80. Dilate(A', Factor, E_1) → A''_3
  81. Dilate(B', Factor, E_1) → B''_4
  82. Dilate(C', Factor, E_1) → C''_3
  83. Polygon(A''_3, B''_4, C''_3) → poly1''_2, c''_3, a''_3, b''_4
  84. Dilate(J, Factor, E_1) → J'_1
  85. Dilate(H, Factor, E_1) → H'_1
  86. Dilate(I, Factor, E_1) → I'_1
  87. Polygon(J'_1, H'_1, I'_1) → poly2'_1, i'_1, j'_1, h'_1
  88. Dilate(A'', Factor, E_1) → A'''
  89. Dilate(B''_1, Factor, E_1) → I_1
  90. Dilate(C'', Factor, E_1) → C'''
  91. Polygon(A''', I_1, C''') → poly1''', c''', a''', i_1
  92. Segment(E_1, C''') → q
  93. Segment(E_1, A''') → r
  94. Segment(E_1, I_1) → t
  95. Segment(J'_1, E_1) → a_1
  96. Segment(I'_1, E_1) → b_1
  97. Segment(H'_1, E_1) → e_1
  98. Dilate(J', Factor, E_1) → J''
  99. Dilate(H', Factor, E_1) → H''
  100. Dilate(I', Factor, E_1) → I''
  101. Polygon(J'', H'', I'') → poly2'', i'', j'', h''
  102. Segment(E_1, H'') → j_1
  103. Segment(E_1, J'') → k_1
  104. Segment(E_1, I'') → l_1
  105. Dilate(Z', Factor, E_1) → Z''
  106. Dilate(C_1, Factor, E_1) → J_1
  107. Dilate(D_1, Factor, E_1) → K_1
  108. Polygon(Z'', J_1, K_1) → poly6', k_2, z'', j_2
  109. Segment(E_1, K_1) → m_1
  110. Segment(E_1, J_1) → n_1
  111. Segment(E_1, Z'') → p_1
  112. Segment(E_1, C''_3) → q_1
  113. Segment(E_1, A''_3) → r_1
  114. Segment(E_1, B''_4) → s_1
  115. Dilate(A''_2, Factor, E_1) → L_1
  116. Dilate(B''_3, Factor, E_1) → M_1
  117. Dilate(C''_2, Factor, E_1) → N_1
  118. Polygon(L_1, M_1, N_1) → poly8, n_2, l_2, m_2
  119. Segment(E_1, L_1) → t_1
  120. Segment(E_1, N_1) → a_2
  121. Segment(E_1, M_1) → b_2
  122. Dilate(U, Factor, E_1) → U'
  123. Dilate(W, Factor, E_1) → W'
  124. Dilate(V, Factor, E_1) → V'
  125. Polygon(U', W', V') → poly5', v', u', w'
  126. Segment(E_1, W') → c_2
  127. Segment(E_1, U') → d_2
  128. Segment(E_1, V') → e_2
  129. Segment(E_1, G_1) → f_2
  130. Segment(E_1, F_1) → g_2
  131. Segment(E_1, H_1) → h_2
  132. Dilate(L, Factor, E_1) → L'
  133. Dilate(M, Factor, E_1) → M'_1
  134. Dilate(N, Factor, E_1) → N'
  135. Polygon(L', M'_1, N') → poly3', n', l', m'_1
  136. Segment(E_1, L') → i_2
  137. Segment(E_1, N') → p_2
  138. Segment(E_1, M'_1) → q_2
  139. Dilate(Q', Factor, E_1) → Q''
  140. Dilate(S, Factor, E_1) → S'
  141. Dilate(R', Factor, E_1) → R''
  142. Polygon(Q'', S', R'') → poly4', r'', q'', s'
  143. Segment(E_1, R'') → r_2
  144. Segment(E_1, S') → s_2
  145. Segment(E_1, Q'') → t_2
  146. Segment(E_1, A'_3) → a_3
  147. Segment(E_1, B'_4) → b_3
  148. Segment(E_1, C'_3) → c_3
  149. Vector(B, B'_4) → w_1
  150. Vector(C, C'_3) → u_2
  151. Vector(A, A'_3) → v_2
  152. Vector(F, G_1) → w_2
  153. Vector(A'_1, F_1) → u_3
  154. Vector(C'_1, H_1) → v_3
  155. Vector(C', C''_3) → w_3
  156. Vector(A', A''_3) → d_3
  157. Vector(B', B''_4) → e_3
  158. Vector(A'_2, H'_1) → f_3
  159. Vector(B'_3, I'_1) → g_3
  160. Vector(C'_2, J'_1) → h_3
  161. Vector(M, M'_1) → i_3
  162. Vector(N, N') → j_3
  163. Vector(L, L') → k_3
  164. Vector(Q, Q'') → l_3
  165. Vector(F'_2, S') → m_3
  166. Vector(R, R'') → n_3
  167. Vector(C''_2, N_1) → p_3
  168. Vector(A''_2, L_1) → q_3
  169. Vector(T, M_1) → r_3
  170. Vector(B''_2, U') → s_3
  171. Vector(C''_1, W') → t_3
  172. Vector(A''_1, V') → u_4
  173. Vector(T, I_1) → v_4
  174. Vector(C'', C''') → w_4
  175. Vector(A'', A''') → a_4
  176. Vector(H', H'') → b_4
  177. Vector(J', J'') → c_4
  178. Vector(I', I'') → d_4
  179. Vector(B_1, K_1) → e_4
  180. Vector(Z, Z'') → f_4
  181. Vector(A_1, J_1) → g_4

AI Drawing Prompt Reference

Create a geometric transformation demonstration showing an initial polygon and a series of transformations: first generate new shapes via reflection and dilation, then produce multiple distorted versions using rotation and vector movement, and finally illustrate symmetry and similarity through further reflections and scalings. The process is controlled by sliders to demonstrate core concepts of geometric transformations, similarity, symmetry, and coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.