MathPlotAI Logo MathPlotAI

Geometric Transformations and Polygons by pfindlay

Geometric Transformations and Polygons by pfindlay
Loading the math board and drawing, please wait…
2014-03-30 14:06
PolygonVectorTransformation
In collections Phebe Tanner Translation Tessallation
This example demonstrates how to use GeoGebra for geometric transformations, including translation, angles, and vectors. By constructing polygons and related elements, students can understand the concepts of geometric transformations and their applications. Main commands used include Line, OrthogonalLine, Point, Intersect, Segment, Angle, Vector, Translate, and Polygon. Suitable for middle school and above students to learn about geometric transformations and polygons.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. OrthogonalLine(A, a) → c
  4. Point(b) → C
  5. OrthogonalLine(C, c) → d
  6. Intersect(c, d) → D
  7. Segment(D, C) → e
  8. Segment(C, B) → f
  9. Segment(B, A) → g
  10. Segment(A, D) → h
  11. Angle(A, B, C) → α
  12. Angle(C, D, A) → β
  13. Angle(D, A, B) → γ
  14. Angle(B, C, D) → δ
  15. Segment(D, E) → i
  16. Segment(E, F) → j
  17. Segment(F, G) → k
  18. Segment(G, H) → l
  19. Segment(H, I) → m
  20. Segment(I, J) → n
  21. Segment(J, K) → p
  22. Segment(K, L) → q
  23. Segment(L, M) → r
  24. Segment(M, C) → s
  25. Vector(C, B) → u
  26. Translate(D, u) → D'
  27. Translate(E, u) → E'
  28. Segment(D', E') → i'
  29. Translate(E, u) → E'_1
  30. Translate(F, u) → F'
  31. Segment(E'_1, F') → j'
  32. Translate(F, u) → F'_1
  33. Translate(G, u) → G'
  34. Segment(F'_1, G') → k'
  35. Translate(G, u) → G'_1
  36. Translate(H, u) → H'
  37. Segment(G'_1, H') → l'
  38. Translate(H, u) → H'_1
  39. Translate(I, u) → I'
  40. Segment(H'_1, I') → m'
  41. Translate(I, u) → I'_1
  42. Translate(J, u) → J'
  43. Segment(I'_1, J') → n'
  44. Translate(J, u) → J'_1
  45. Translate(K, u) → K'
  46. Segment(J'_1, K') → p'
  47. Translate(K, u) → K'_1
  48. Translate(L, u) → L'
  49. Segment(K'_1, L') → q'
  50. Translate(L, u) → L'_1
  51. Translate(M, u) → M'
  52. Segment(L'_1, M') → r'
  53. Translate(M, u) → M'_1
  54. Translate(C, u) → C'
  55. Segment(M'_1, C') → s'
  56. Segment(D, N) → t
  57. Segment(N, O) → a_1
  58. Segment(O, P) → b_1
  59. Segment(P, Q) → c_1
  60. Segment(Q, R) → d_1
  61. Segment(R, S) → e_1
  62. Segment(S, T) → f_1
  63. Segment(T, U) → g_1
  64. Segment(U, V) → h_1
  65. Segment(V, W) → i_1
  66. Segment(W, Z) → j_1
  67. Segment(Z, A) → k_1
  68. Vector(A, B) → v
  69. Translate(D, v) → D'_1
  70. Translate(N, v) → N'
  71. Segment(D'_1, N') → t'
  72. Translate(N, v) → N'_1
  73. Translate(O, v) → O'
  74. Segment(N'_1, O') → l_1
  75. Translate(O, v) → O'_1
  76. Translate(P, v) → P'
  77. Segment(O'_1, P') → m_1
  78. Translate(P, v) → P'_1
  79. Translate(Q, v) → Q'
  80. Segment(P'_1, Q') → n_1
  81. Translate(Q, v) → Q'_1
  82. Translate(R, v) → R'
  83. Segment(Q'_1, R') → p_1
  84. Translate(R, v) → R'_1
  85. Translate(S, v) → S'
  86. Segment(R'_1, S') → q_1
  87. Translate(S, v) → S'_1
  88. Translate(T, v) → T'
  89. Segment(S'_1, T') → r_1
  90. Translate(T, v) → T'_1
  91. Translate(U, v) → U'
  92. Segment(T'_1, U') → s_1
  93. Translate(U, v) → U'_1
  94. Translate(V, v) → V'
  95. Segment(U'_1, V') → t_1
  96. Translate(V, v) → V'_1
  97. Translate(W, v) → W'
  98. Segment(V'_1, W') → a_2
  99. Translate(W, v) → W'_1
  100. Translate(Z, v) → Z'
  101. Segment(W'_1, Z') → b_2
  102. Translate(Z, v) → Z'_1
  103. Translate(A, v) → A'
  104. Segment(Z'_1, A') → c_2
  105. Translate(D', v) → D''
  106. Intersect(j_1, k_1) → A_1
  107. Point(i_1) → B_1
  108. Intersect(h_1, i_1) → C_1
  109. Intersect(g_1, h_1) → D_1
  110. Intersect(f_1, g_1) → E_1
  111. Point(e_1) → F_1
  112. Intersect(d_1, e_1) → G_1
  113. Intersect(c_1, d_1) → H_1
  114. Intersect(b_1, c_1) → I_1
  115. Intersect(t, a_1) → J_1
  116. Intersect(i, t) → K_1
  117. Intersect(i, j) → L_1
  118. Intersect(i', k_1) → M_1
  119. Intersect(j_1, k_1) → N_1
  120. Intersect(i_1, j_1) → O_1
  121. Point(i_1) → P_1
  122. Intersect(g_1, h_1) → Q_1
  123. Intersect(f_1, g_1) → R_1
  124. Intersect(d_1, e_1) → S_1
  125. Intersect(c_1, d_1) → T_1
  126. Intersect(b_1, c_1) → U_1
  127. Intersect(t, a_1) → V_1
  128. Intersect(i, t) → W_1
  129. Intersect(i, j) → Z_1
  130. Intersect(j, k) → A_2
  131. Intersect(k, l) → B_2
  132. Intersect(l, m) → C_2
  133. Intersect(m, n) → D_2
  134. Intersect(n, p) → E_2
  135. Point(q) → F_2
  136. Intersect(r, s) → G_2
  137. Intersect(s, t') → H_2
  138. Intersect(t', l_1) → I_2
  139. Intersect(m_1, n_1) → J_2
  140. Intersect(n_1, p_1) → K_2
  141. Intersect(p_1, q_1) → L_2
  142. Intersect(q_1, r_1) → M_2
  143. Intersect(r_1, s_1) → N_2
  144. Intersect(s_1, t_1) → O_2
  145. Intersect(t_1, a_2) → P_2
  146. Intersect(a_2, b_2) → Q_2
  147. Intersect(b_2, c_2) → R_2
  148. Intersect(s', c_2) → S_2
  149. Intersect(r', s') → T_2
  150. Point(q') → U_2
  151. Intersect(n', p') → V_2
  152. Intersect(m', n') → W_2
  153. Intersect(l', m') → Z_2
  154. Point(l') → A_3
  155. Intersect(j', k') → B_3
  156. Intersect(i', j') → C_3
  157. Polygon(M_1, N_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, O_1, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, P_1, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, Q_1, R_1, S_1, T_1, U_1, V_1) → poly1, m_2, v_1, w_1, z_1, a_3, b_3, c_3, d_2, e_2, f_2, g_2, n_2, h_2, i_2, j_2, k_2, l_2, m_3, n_3, o_2, p_3, q_3, o_1, r_3, s_3, t_3, u_2, v_2, w_2, z_2, a_4, b_4, c_4, p_2, q_2, r_2, s_2, t_2, u_1
  158. Segment(R_1, D_3) → d_3
  159. Segment(D_3, B_3) → e_3
  160. Polygon(D_3, R_1, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, S_1, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, T_1, W_2, Z_2, A_3, B_3, U_1, V_1, W_1, Z_1, A_2, B_2) → poly2, d_4, b_5, c_5, d_5, e_4, f_3, g_3, h_3, i_3, j_3, k_3, r_4, l_3, m_4, n_4, o_3, p_4, q_4, r_5, s_5, t_5, u_4, s_4, v_4, w_4, z_4, a_6, b_6, t_4, u_3, v_3, w_3, z_3, a_5
  161. Segment(M_1, O_1) → f_4
  162. Polygon(M_1, N_1, O_1) → poly3, o_4, m_5, n_5
  163. Vector(A, B) → w
  164. Translate(M_1, w) → F_3
  165. Translate(N_1, w) → G_3
  166. Translate(O_1, w) → H_3
  167. Translate(P_1, w) → I_3
  168. Translate(Q_1, w) → J_3
  169. Translate(R_1, w) → K_3
  170. Translate(S_1, w) → L_3
  171. Translate(T_1, w) → M_3
  172. Translate(U_1, w) → N_3
  173. Translate(V_1, w) → O_3
  174. Translate(W_1, w) → P_3
  175. Translate(Z_1, w) → Q_3
  176. Translate(A_2, w) → R_3
  177. Translate(B_2, w) → S_3
  178. Translate(C_2, w) → T_3
  179. Translate(D_2, w) → U_3
  180. Translate(E_2, w) → V_3
  181. Translate(F_2, w) → W_3
  182. Translate(G_2, w) → Z_3
  183. Translate(H_2, w) → A_4
  184. Translate(I_2, w) → B_4
  185. Translate(J_2, w) → C_4
  186. Translate(K_2, w) → D_4
  187. Translate(L_2, w) → E_4
  188. Translate(M_2, w) → F_4
  189. Translate(N_2, w) → G_4
  190. Translate(O_2, w) → H_4
  191. Translate(P_2, w) → I_4
  192. Translate(Q_2, w) → J_4
  193. Translate(R_2, w) → K_4
  194. Translate(S_2, w) → L_4
  195. Translate(T_2, w) → M_4
  196. Translate(U_2, w) → N_4
  197. Translate(V_2, w) → O_4
  198. Translate(W_2, w) → P_4
  199. Translate(Z_2, w) → Q_4
  200. Translate(A_3, w) → R_4
  201. Translate(B_3, w) → S_4
  202. Translate(C_3, w) → T_4
  203. Polygon(F_3, G_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, H_3, B_4, C_4, D_4, E_4, F_4, G_4, H_4, I_4, J_4, K_4, I_3, L_4, M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4, J_3, K_3, L_3, M_3, N_3, O_3) → poly1', f_5, o_5, p_5, q_5, r_6, s_6, t_6, u_5, v_5, w_5, z_5, g_4, a_7, b_7, c_6, d_6, e_5, f_6, g_5, h_5, i_5, j_5, h_4, k_5, l_5, m_7, n_7, o_6, p_6, q_6, r_7, s_7, t_7, i_4, j_4, k_4, l_4, m_6, n_6
  204. Translate(D_3, w) → U_4
  205. Translate(R_1, w) → V_4
  206. Translate(S_1, w) → W_4
  207. Translate(T_1, w) → Z_4
  208. Translate(U_1, w) → A_5
  209. Translate(V_1, w) → B_5
  210. Translate(W_1, w) → C_5
  211. Translate(Z_1, w) → D_5
  212. Translate(A_2, w) → E_5
  213. Translate(B_2, w) → F_5
  214. Translate(C_2, w) → G_5
  215. Translate(D_2, w) → H_5
  216. Translate(E_2, w) → I_5
  217. Translate(F_2, w) → J_5
  218. Translate(G_2, w) → K_5
  219. Translate(H_2, w) → L_5
  220. Translate(I_2, w) → M_5
  221. Translate(J_2, w) → N_5
  222. Translate(K_2, w) → O_5
  223. Translate(L_2, w) → P_5
  224. Translate(M_2, w) → Q_5
  225. Translate(N_2, w) → R_5
  226. Translate(O_2, w) → S_5
  227. Translate(P_2, w) → T_5
  228. Translate(Q_2, w) → U_5
  229. Translate(R_2, w) → V_5
  230. Translate(S_2, w) → W_5
  231. Translate(T_2, w) → Z_5
  232. Translate(U_2, w) → A_6
  233. Translate(V_2, w) → B_6
  234. Translate(W_2, w) → C_6
  235. Translate(Z_2, w) → D_6
  236. Translate(A_3, w) → E_6
  237. Translate(B_3, w) → F_6
  238. Polygon(U_4, V_4, G_5, H_5, I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, W_4, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6, Z_4, C_6, D_6, E_6, F_6, A_5, B_5, C_5, D_5, E_5, F_5) → poly2', u_6, f_7, g_6, h_6, i_6, j_6, k_6, l_6, m_8, n_8, o_7, v_6, p_7, q_7, r_8, s_8, t_8, u_7, v_7, w_7, z_7, a_9, w_6, b_9, c_8, d_8, e_7, f_8, z_6, a_8, b_8, c_7, d_7, e_6
  239. Translate(M_1, w) → G_6
  240. Translate(N_1, w) → H_6
  241. Translate(O_1, w) → I_6
  242. Polygon(G_6, H_6, I_6) → poly3', i_7, g_7, h_7
  243. Translate(D, w) → D'_2
  244. Translate(E, w) → E'_2
  245. Segment(D'_2, E'_2) → i'_1
  246. Translate(E, w) → E'_3
  247. Translate(F, w) → F'_2
  248. Segment(E'_3, F'_2) → j'_1
  249. Translate(F, w) → F'_3
  250. Translate(G, w) → G'_2
  251. Segment(F'_3, G'_2) → k'_1
  252. Translate(G, w) → G'_3
  253. Translate(H, w) → H'_2
  254. Segment(G'_3, H'_2) → l'_1
  255. Translate(H, w) → H'_3
  256. Translate(I, w) → I'_2
  257. Segment(H'_3, I'_2) → m'_1
  258. Translate(I, w) → I'_3
  259. Translate(J, w) → J'_2
  260. Segment(I'_3, J'_2) → n'_1
  261. Translate(J, w) → J'_3
  262. Translate(K, w) → K'_2
  263. Segment(J'_3, K'_2) → p'_1
  264. Translate(K, w) → K'_3
  265. Translate(L, w) → L'_2
  266. Segment(K'_3, L'_2) → q'_1
  267. Translate(L, w) → L'_3
  268. Translate(M, w) → M'_2
  269. Segment(L'_3, M'_2) → r'_1
  270. Translate(M, w) → M'_3
  271. Translate(C, w) → C'_1
  272. Segment(M'_3, C'_1) → s'_1
  273. Translate(D', w) → D''_1
  274. Translate(E', w) → E''
  275. Segment(D''_1, E'') → i''
  276. Translate(E'_1, w) → J_6
  277. Translate(F', w) → F''
  278. Segment(J_6, F'') → j''
  279. Translate(F'_1, w) → K_6
  280. Translate(G', w) → G''
  281. Segment(K_6, G'') → k''
  282. Translate(G'_1, w) → L_6
  283. Translate(H', w) → H''
  284. Segment(L_6, H'') → l''
  285. Translate(H'_1, w) → M_6
  286. Translate(I', w) → I''
  287. Segment(M_6, I'') → m''
  288. Translate(I'_1, w) → N_6
  289. Translate(J', w) → J''
  290. Segment(N_6, J'') → n''
  291. Translate(J'_1, w) → O_6
  292. Translate(K', w) → K''
  293. Segment(O_6, K'') → p''
  294. Translate(K'_1, w) → P_6
  295. Translate(L', w) → L''
  296. Segment(P_6, L'') → q''
  297. Translate(L'_1, w) → Q_6
  298. Translate(M', w) → M''
  299. Segment(Q_6, M'') → r''
  300. Translate(M'_1, w) → R_6
  301. Translate(C', w) → C''
  302. Segment(R_6, C'') → s''
  303. Translate(D, w) → D'_3
  304. Translate(N, w) → N'_2
  305. Segment(D'_3, N'_2) → t'_1
  306. Translate(N, w) → N'_3
  307. Translate(O, w) → O'_2
  308. Segment(N'_3, O'_2) → j_7
  309. Translate(O, w) → O'_3
  310. Translate(P, w) → P'_2
  311. Segment(O'_3, P'_2) → k_7
  312. Translate(P, w) → P'_3
  313. Translate(Q, w) → Q'_2
  314. Segment(P'_3, Q'_2) → l_7
  315. Translate(Q, w) → Q'_3
  316. Translate(R, w) → R'_2
  317. Segment(Q'_3, R'_2) → e_8
  318. Translate(R, w) → R'_3
  319. Translate(S, w) → S'_2
  320. Segment(R'_3, S'_2) → g_8
  321. Translate(S, w) → S'_3
  322. Translate(T, w) → T'_2
  323. Segment(S'_3, T'_2) → h_8
  324. Translate(T, w) → T'_3
  325. Translate(U, w) → U'_2
  326. Segment(T'_3, U'_2) → i_8
  327. Translate(U, w) → U'_3
  328. Translate(V, w) → V'_2
  329. Segment(U'_3, V'_2) → j_8
  330. Translate(V, w) → V'_3
  331. Translate(W, w) → W'_2
  332. Segment(V'_3, W'_2) → k_8
  333. Translate(W, w) → W'_3
  334. Translate(Z, w) → Z'_2
  335. Segment(W'_3, Z'_2) → l_8
  336. Translate(Z, w) → Z'_3
  337. Translate(A, w) → A'_1
  338. Segment(Z'_3, A'_1) → p_8
  339. Translate(D'_1, w) → S_6
  340. Translate(N', w) → N''
  341. Segment(S_6, N'') → t''
  342. Translate(N'_1, w) → T_6
  343. Translate(O', w) → O''
  344. Segment(T_6, O'') → q_8
  345. Translate(O'_1, w) → U_6
  346. Translate(P', w) → P''
  347. Segment(U_6, P'') → c_9
  348. Translate(P'_1, w) → V_6
  349. Translate(Q', w) → Q''
  350. Segment(V_6, Q'') → d_9
  351. Translate(Q'_1, w) → W_6
  352. Translate(R', w) → R''
  353. Segment(W_6, R'') → e_9
  354. Translate(R'_1, w) → Z_6
  355. Translate(S', w) → S''
  356. Segment(Z_6, S'') → f_9
  357. Translate(S'_1, w) → A_7
  358. Translate(T', w) → T''
  359. Segment(A_7, T'') → g_9
  360. Translate(T'_1, w) → B_7
  361. Translate(U', w) → U''
  362. Segment(B_7, U'') → h_9
  363. Translate(U'_1, w) → C_7
  364. Translate(V', w) → V''
  365. Segment(C_7, V'') → i_9
  366. Translate(V'_1, w) → D_7
  367. Translate(W', w) → W''
  368. Segment(D_7, W'') → j_9
  369. Translate(W'_1, w) → E_7
  370. Translate(Z', w) → Z''
  371. Segment(E_7, Z'') → k_9
  372. Translate(Z'_1, w) → F_7
  373. Translate(A', w) → A''
  374. Segment(F_7, A'') → l_9
  375. Translate(R_1, w) → G_7
  376. Translate(D_3, w) → H_7
  377. Segment(G_7, H_7) → m_9
  378. Translate(D_3, w) → I_7
  379. Translate(B_3, w) → J_7
  380. Segment(I_7, J_7) → n_9
  381. Translate(M_1, w) → K_7
  382. Translate(O_1, w) → L_7
  383. Segment(K_7, L_7) → p_9
  384. Translate(E_3, w) → M_7

AI Drawing Prompt Reference

Draw a complex geometric figure composed of multiple regular polygons, start by constructing a square and finding its center point, then draw perpendicular lines from the center to each side of the square, the intersection points form a new square, next, use these intersection points as vertices to draw new regular polygons, and use a vector to translate one vertex along the side length, translate all vertices in sequence to form a series of translated regular polygons, demonstrating the principles of geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.