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Exploring Rotations by brotheas

Exploring Rotations by brotheas
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2013-04-30 12:09
AngleCoordinate GeometryTransformationGeometric Construction
In collections Rotations in the coordinate plane Rotations
This example demonstrates the effects of rotations around the origin on geometric figures. Core math concepts include rotation transformation, angle measurement, and coordinate geometry. It utilizes commands and objects such as Segment, Point, Mirror, Line, Intersect, Rotate, and Angle in GeoGebra. Suitable for high school students learning geometric transformations or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Segment(C, A) → a
  2. Segment(D, B) → b
  3. Segment(B, E) → c
  4. Point(xAxis) → F
  5. Point(xAxis) → G
  6. Segment(F, G) → g
  7. Mirror(C, g) → C'
  8. Mirror(A, g) → A'
  9. Segment(C', A') → a'
  10. Mirror(D, g) → D'
  11. Mirror(B, g) → B'
  12. Segment(D', B') → b'
  13. Mirror(B, g) → B'_1
  14. Mirror(E, g) → E'
  15. Segment(B'_1, E') → c'
  16. Segment(I, H) → l
  17. Segment(J, K) → m
  18. Point(l) → L
  19. Point(m) → M
  20. Segment(L, M) → n
  21. Mirror(I, g) → I'
  22. Mirror(H, g) → H'
  23. Segment(I', H') → l'
  24. Mirror(J, g) → J'
  25. Mirror(K, g) → K'
  26. Segment(J', K') → m'
  27. Mirror(L, g) → L'
  28. Mirror(M, g) → M'
  29. Segment(L', M') → n'
  30. Segment(N, O) → p
  31. Segment(O, P) → q
  32. Segment(P, S) → r
  33. Segment(Q, R) → s
  34. Mirror(N, g) → N'
  35. Mirror(O, g) → O'
  36. Segment(N', O') → p'
  37. Mirror(O, g) → O'_1
  38. Mirror(P, g) → P'
  39. Segment(O'_1, P') → q'
  40. Mirror(P, g) → P'_1
  41. Mirror(S, g) → S'
  42. Segment(P'_1, S') → r'
  43. Mirror(Q, g) → Q'
  44. Mirror(R, g) → R'
  45. Segment(Q', R') → s'
  46. Point(yAxis) → T
  47. Point(yAxis) → U
  48. Segment(T, U) → t
  49. Mirror(C, yAxis) → C'_1
  50. Mirror(A, yAxis) → A'_1
  51. Segment(C'_1, A'_1) → a'_1
  52. Mirror(D, yAxis) → D'_1
  53. Mirror(B, yAxis) → B'_2
  54. Segment(D'_1, B'_2) → b'_1
  55. Mirror(B, yAxis) → B'_3
  56. Mirror(E, yAxis) → E'_1
  57. Segment(B'_3, E'_1) → c'_1
  58. Mirror(I, t) → I'_1
  59. Mirror(H, t) → H'_1
  60. Segment(I'_1, H'_1) → l'_1
  61. Mirror(J, t) → J'_1
  62. Mirror(K, t) → K'_1
  63. Segment(J'_1, K'_1) → m'_1
  64. Mirror(L, t) → L'_1
  65. Mirror(M, t) → M'_1
  66. Segment(L'_1, M'_1) → n'_1
  67. Mirror(N, yAxis) → N'_1
  68. Mirror(O, yAxis) → O'_2
  69. Segment(N'_1, O'_2) → p'_1
  70. Mirror(O, yAxis) → O'_3
  71. Mirror(P, yAxis) → P'_2
  72. Segment(O'_3, P'_2) → q'_1
  73. Mirror(P, yAxis) → P'_3
  74. Mirror(S, yAxis) → S'_1
  75. Segment(P'_3, S'_1) → r'_1
  76. Mirror(Q, yAxis) → Q'_1
  77. Mirror(R, yAxis) → R'_1
  78. Segment(Q'_1, R'_1) → s'_1
  79. Line(V, W) → a_1
  80. Mirror(C, a_1) → C'_2
  81. Mirror(A, a_1) → A'_2
  82. Segment(C'_2, A'_2) → a'_2
  83. Mirror(D, a_1) → D'_2
  84. Mirror(B, a_1) → B'_4
  85. Segment(D'_2, B'_4) → b'_2
  86. Mirror(B, a_1) → B'_5
  87. Mirror(E, a_1) → E'_2
  88. Segment(B'_5, E'_2) → c'_2
  89. Mirror(I, a_1) → I'_2
  90. Mirror(H, a_1) → H'_2
  91. Segment(I'_2, H'_2) → l'_2
  92. Mirror(J, a_1) → J'_2
  93. Mirror(K, a_1) → K'_2
  94. Segment(J'_2, K'_2) → m'_2
  95. Mirror(L, a_1) → L'_2
  96. Mirror(M, a_1) → M'_2
  97. Segment(L'_2, M'_2) → n'_2
  98. Mirror(N, a_1) → N'_2
  99. Mirror(O, a_1) → O'_4
  100. Segment(N'_2, O'_4) → p'_2
  101. Mirror(O, a_1) → O'_5
  102. Mirror(P, a_1) → P'_4
  103. Segment(O'_5, P'_4) → q'_2
  104. Mirror(P, a_1) → P'_5
  105. Mirror(S, a_1) → S'_2
  106. Segment(P'_5, S'_2) → r'_2
  107. Mirror(Q, a_1) → Q'_2
  108. Mirror(R, a_1) → R'_2
  109. Segment(Q'_2, R'_2) → s'_2
  110. Line(Z, A_1) → b_1
  111. Mirror(N, b_1) → N'_3
  112. Mirror(O, b_1) → O'_6
  113. Segment(N'_3, O'_6) → p'_3
  114. Mirror(O, b_1) → O'_7
  115. Mirror(P, b_1) → P'_6
  116. Segment(O'_7, P'_6) → q'_3
  117. Mirror(P, b_1) → P'_7
  118. Mirror(S, b_1) → S'_3
  119. Segment(P'_7, S'_3) → r'_3
  120. Mirror(Q, b_1) → Q'_3
  121. Mirror(R, b_1) → R'_3
  122. Segment(Q'_3, R'_3) → s'_3
  123. Mirror(I, b_1) → I'_3
  124. Mirror(H, b_1) → H'_3
  125. Segment(I'_3, H'_3) → l'_3
  126. Mirror(J, b_1) → J'_3
  127. Mirror(K, b_1) → K'_3
  128. Segment(J'_3, K'_3) → m'_3
  129. Mirror(L, b_1) → L'_3
  130. Mirror(M, b_1) → M'_3
  131. Segment(L'_3, M'_3) → n'_3
  132. Mirror(C, b_1) → C'_3
  133. Mirror(A, b_1) → A'_3
  134. Segment(C'_3, A'_3) → a'_3
  135. Mirror(D, b_1) → D'_3
  136. Mirror(B, b_1) → B'_6
  137. Segment(D'_3, B'_6) → b'_3
  138. Mirror(B, b_1) → B'_7
  139. Mirror(E, b_1) → E'_3
  140. Segment(B'_7, E'_3) → c'_3
  141. Intersect(xAxis, yAxis) → B_1
  142. Rotate(C, 270*°, B_1) → C'_4
  143. Rotate(A, 270*°, B_1) → A'_4
  144. Segment(C'_4, A'_4) → a'_4
  145. Rotate(D, 270*°, B_1) → D'_4
  146. Rotate(B, 270*°, B_1) → B'_8
  147. Segment(D'_4, B'_8) → b'_4
  148. Rotate(B, 270*°, B_1) → B'_9
  149. Rotate(E, 270*°, B_1) → E'_4
  150. Segment(B'_9, E'_4) → c'_4
  151. Rotate(C, 180*°, B_1) → C'_5
  152. Rotate(A, 180*°, B_1) → A'_5
  153. Segment(C'_5, A'_5) → a'_5
  154. Rotate(D, 180*°, B_1) → D'_5
  155. Rotate(B, 180*°, B_1) → B'_{10}
  156. Segment(D'_5, B'_{10}) → b'_5
  157. Rotate(B, 180*°, B_1) → B'_{11}
  158. Rotate(E, 180*°, B_1) → E'_5
  159. Segment(B'_{11}, E'_5) → c'_5
  160. Rotate(C, 90*°, B_1) → C'_6
  161. Rotate(A, 90*°, B_1) → A'_6
  162. Segment(C'_6, A'_6) → a'_6
  163. Rotate(D, 90*°, B_1) → D'_6
  164. Rotate(B, 90*°, B_1) → B'_{12}
  165. Segment(D'_6, B'_{12}) → b'_6
  166. Rotate(B, 90*°, B_1) → B'_{13}
  167. Rotate(E, 90*°, B_1) → E'_6
  168. Segment(B'_{13}, E'_6) → c'_6
  169. Rotate(I, 90*°, B_1) → I'_4
  170. Rotate(H, 90*°, B_1) → H'_4
  171. Segment(I'_4, H'_4) → l'_4
  172. Rotate(J, 90*°, B_1) → J'_4
  173. Rotate(K, 90*°, B_1) → K'_4
  174. Segment(J'_4, K'_4) → m'_4
  175. Rotate(L, 90*°, B_1) → L'_4
  176. Rotate(M, 90*°, B_1) → M'_4
  177. Segment(L'_4, M'_4) → n'_4
  178. Rotate(I, 180*°, B_1) → I'_5
  179. Rotate(H, 180*°, B_1) → H'_5
  180. Segment(I'_5, H'_5) → l'_5
  181. Rotate(J, 180*°, B_1) → J'_5
  182. Rotate(K, 180*°, B_1) → K'_5
  183. Segment(J'_5, K'_5) → m'_5
  184. Rotate(L, 180*°, B_1) → L'_5
  185. Rotate(M, 180*°, B_1) → M'_5
  186. Segment(L'_5, M'_5) → n'_5
  187. Rotate(I, 270*°, B_1) → I'_6
  188. Rotate(H, 270*°, B_1) → H'_6
  189. Segment(I'_6, H'_6) → l'_6
  190. Rotate(J, 270*°, B_1) → J'_6
  191. Rotate(K, 270*°, B_1) → K'_6
  192. Segment(J'_6, K'_6) → m'_6
  193. Rotate(L, 270*°, B_1) → L'_6
  194. Rotate(M, 270*°, B_1) → M'_6
  195. Segment(L'_6, M'_6) → n'_6
  196. Rotate(N, 270*°, B_1) → N'_4
  197. Rotate(O, 270*°, B_1) → O'_8
  198. Segment(N'_4, O'_8) → p'_4
  199. Rotate(O, 270*°, B_1) → O'_9
  200. Rotate(P, 270*°, B_1) → P'_8
  201. Segment(O'_9, P'_8) → q'_4
  202. Rotate(P, 270*°, B_1) → P'_9
  203. Rotate(S, 270*°, B_1) → S'_4
  204. Segment(P'_9, S'_4) → r'_4
  205. Rotate(Q, 270*°, B_1) → Q'_4
  206. Rotate(R, 270*°, B_1) → R'_4
  207. Segment(Q'_4, R'_4) → s'_4
  208. Rotate(N'_4, 270*°, B_1) → C_1
  209. Rotate(O'_8, 270*°, B_1) → D_1
  210. Segment(C_1, D_1) → d_1
  211. Rotate(O'_9, 270*°, B_1) → E_1
  212. Rotate(P'_8, 270*°, B_1) → F_1
  213. Segment(E_1, F_1) → e_1
  214. Rotate(P'_9, 270*°, B_1) → G_1
  215. Rotate(S'_4, 270*°, B_1) → H_1
  216. Segment(G_1, H_1) → f_1
  217. Rotate(Q'_4, 270*°, B_1) → I_1
  218. Rotate(R'_4, 270*°, B_1) → J_1
  219. Segment(I_1, J_1) → g_1
  220. Rotate(C_1, 270*°, B_1) → K_1
  221. Rotate(D_1, 270*°, B_1) → L_1
  222. Segment(K_1, L_1) → h_1
  223. Rotate(E_1, 270*°, B_1) → M_1
  224. Rotate(F_1, 270*°, B_1) → N_1
  225. Segment(M_1, N_1) → i_1
  226. Rotate(G_1, 270*°, B_1) → O_1
  227. Rotate(H_1, 270*°, B_1) → P_1
  228. Segment(O_1, P_1) → j_1
  229. Rotate(I_1, 270*°, B_1) → Q_1
  230. Rotate(J_1, 270*°, B_1) → R_1
  231. Segment(Q_1, R_1) → k_1
  232. Segment(C, B_1) → l_1
  233. Segment(B_1, C'_4) → m_1
  234. Angle(C'_4, B_1, C) → α
  235. Segment(C'_5, B_1) → n_1
  236. Segment(B_1, C) → p_1
  237. Angle(C'_5, B_1, C) → β
  238. Segment(C'_6, B_1) → q_1
  239. Segment(B_1, C) → r_1
  240. Angle(C'_6, B_1, C) → γ
  241. Segment(J, B_1) → s_1
  242. Segment(B_1, J'_6) → t_1
  243. Angle(J'_6, B_1, J) → δ
  244. Segment(J, B_1) → a_2
  245. Segment(B_1, J'_5) → b_2
  246. Angle(J'_5, B_1, J) → ε
  247. Segment(J, B_1) → c_2
  248. Segment(B_1, J'_4) → d_2
  249. Angle(J'_4, B_1, J) → ζ
  250. Segment(O'_8, B_1) → e_2
  251. Segment(O, B_1) → f_2
  252. Angle(O'_8, B_1, O) → η
  253. Segment(D_1, B_1) → g_2
  254. Segment(O, B_1) → h_2
  255. Angle(D_1, B_1, O) → θ
  256. Segment(L_1, B_1) → i_2
  257. Segment(B_1, O) → j_2
  258. Angle(L_1, B_1, O) → ι

AI Drawing Prompt Reference

Draw a geometric figure to demonstrate the effects of rotations around the origin. Start by drawing two line segments and their reflections, then draw the reflected line segments. Next, draw the coordinate axes and use them to perform mirror operations, obtaining new line segments. Finally, draw the coordinate axes and connect two points to form a line segment, fully showcasing the geometric transformation process of rotation and reflection.
The prompt above was compiled from the original drawing commands and is for reference only.