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Adjustable Angle and Inclination of Line Segment

Adjustable Angle and Inclination of Line Segment
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2020-03-08 01:31
AngleTransformationGeometric Construction
This example demonstrates how to adjust the angle and inclination of a line segment through rotation and tilting. Key mathematical concepts include angles, rotation, and geometric transformations. Using GeoGebra commands such as Rotate, Ray, and Intersect, the direction and position of the line segment can be dynamically changed. Suitable for middle school and above students to learn about geometric transformations and angle-related problems.

GeoGebra Commands & Parameters

  1. Line(P0, A) → rt0
  2. Rotate(A, θ, P0) → A1
  3. Line(P0, A1) → rt1
  4. Rotate(B1, α, P1) → C1
  5. Ray(P1, C1) → sr1
  6. Intersect(rt1, sr1) → F1
  7. Circle(P0, F1) → c1
  8. If(x(F1) < x(P0), 1, 2) → SnDx1
  9. Intersect(c1, rt0, SnDx1) → P2
  10. Rotate(B2, α + γ, P2) → C2
  11. Ray(P2, C2) → sr2
  12. Intersect(rt1, sr2) → F2
  13. Rotate(F2, θ, P0) → W2
  14. If(x(F2) < x(P0), 1, 2) → SnDx2
  15. Circle(P0, F2) → c2
  16. Intersect(c2, rt0, SnDx2) → P3
  17. Rotate(B3, α + (2 * γ), P3) → C3
  18. Ray(P3, C3) → sr3
  19. Intersect(rt1, sr3) → F3
  20. Rotate(F3, (2 * θ), P0) → W3
  21. Circle(P0, F3) → c3
  22. If(x(F3) < x(P0), 1, 2) → SnDx3
  23. Intersect(c3, rt0, SnDx3) → P4
  24. Rotate(B4, α + (3 * γ), P4) → C4
  25. Ray(P4, C4) → sr4
  26. Intersect(rt1, sr4) → F4
  27. Rotate(F4, (3 * θ), P0) → W4
  28. If(x(F4) < x(P0), 1, 2) → SnDx4
  29. Circle(P0, F4) → c4
  30. Intersect(c4, rt0, SnDx4) → P5
  31. Rotate(B5, α + (4 * γ), P5) → C5
  32. Ray(P5, C5) → sr5
  33. Intersect(rt1, sr5) → F5
  34. Rotate(F5, (4 * θ), P0) → W5
  35. Circle(P0, F5) → c5
  36. If(x(F5) < x(P0), 1, 2) → SnDx5
  37. Intersect(c5, rt0, SnDx5) → P6
  38. Rotate(B6, α + (5 * γ), P6) → C6
  39. Ray(P6, C6) → sr6
  40. Intersect(rt1, sr6) → F6
  41. Rotate(F6, (5 * θ), P0) → W6
  42. If(x(F6) < x(P0), 1, 2) → SnDx6
  43. Circle(P0, F6) → c6
  44. Intersect(c6, rt0, SnDx6) → P7
  45. Rotate(B7, α + (6 * γ), P7) → C7
  46. Ray(P7, C7) → sr7
  47. Intersect(rt1, sr7) → F7
  48. Rotate(F7, (6 * θ), P0) → W7
  49. Circle(P0, F7) → c7
  50. If(x(F7) < x(P0), 1, 2) → SnDx7
  51. Intersect(c7, rt0, SnDx7) → P8
  52. Rotate(B8, α + (7 * γ), P8) → C8
  53. Ray(P8, C8) → sr8
  54. Intersect(rt1, sr8) → F8
  55. Rotate(F8, (7 * θ), P0) → W8
  56. If(x(F8) < x(P0), 1, 2) → SnDx8
  57. Circle(P0, F8) → c8
  58. Intersect(c8, rt0, SnDx8) → P9
  59. Rotate(B9, α + (8 * γ), P9) → C9
  60. Ray(P9, C9) → sr9
  61. Intersect(rt1, sr9) → F9
  62. Rotate(F9, (8 * θ), P0) → W9
  63. Circle(P0, F9) → c9
  64. If(x(F9) < x(P0), 1, 2) → SnDx9
  65. Intersect(c9, rt0, SnDx9) → P10
  66. Rotate(B10, α + (9 * γ), P10) → C10
  67. Ray(P10, C10) → sr10
  68. Intersect(rt1, sr10) → F10
  69. Rotate(F10, (9 * θ), P0) → W10
  70. If(x(F10) < x(P0), 1, 2) → SnDx10
  71. Circle(P0, F10) → c10
  72. Intersect(c10, rt0, SnDx10) → P11
  73. Rotate(B11, α + (10 * γ), P11) → C11
  74. Ray(P11, C11) → sr11
  75. Intersect(rt1, sr11) → F11
  76. Rotate(F11, (10 * θ), P0) → W11
  77. Circle(P0, F11) → c11
  78. If(x(F11) < x(P0), 1, 2) → SnDx11
  79. Intersect(c11, rt0, SnDx11) → P12
  80. Rotate(B12, α + (11 * γ), P12) → C12
  81. Ray(P12, C12) → sr12
  82. Intersect(rt1, sr12) → F12
  83. Rotate(F12, (11 * θ), P0) → W12
  84. If(x(F12) < x(P0), 1, 2) → SnDx12
  85. Circle(P0, F12) → c12
  86. Intersect(c12, rt0, SnDx12) → P13
  87. Rotate(B13, α + (12 * γ), P13) → C13
  88. Ray(P13, C13) → sr13
  89. Intersect(rt1, sr13) → F13
  90. Rotate(F13, (12 * θ), P0) → W13
  91. Circle(P0, F13) → c13
  92. If(x(F13) < x(P0), 1, 2) → SnDx13
  93. Intersect(c13, rt0, SnDx13) → P14
  94. Rotate(B14, α + (13 * γ), P14) → C14
  95. Ray(P14, C14) → sr14
  96. Intersect(rt1, sr14) → F14
  97. Rotate(F14, (13 * θ), P0) → W14
  98. If(x(F14) < x(P0), 1, 2) → SnDx14
  99. Circle(P0, F14) → c14
  100. Intersect(c14, rt0, SnDx14) → P15
  101. Rotate(B15, α + (14 * γ), P15) → C15
  102. Ray(P15, C15) → sr15
  103. Intersect(rt1, sr15) → F15
  104. Rotate(F15, (14 * θ), P0) → W15
  105. Circle(P0, F15) → c15
  106. If(x(F15) < x(P0), 1, 2) → SnDx15
  107. Intersect(c15, rt0, SnDx15) → P16
  108. Rotate(B16, α + (15 * γ), P16) → C16
  109. Ray(P16, C16) → sr16
  110. Intersect(rt1, sr16) → F16
  111. Rotate(F16, (15 * θ), P0) → W16
  112. If(x(F16) < x(P0), 1, 2) → SnDx16
  113. Circle(P0, F16) → c16
  114. Intersect(c16, rt0, SnDx16) → P17
  115. Rotate(B17, α + (16 * γ), P17) → C17
  116. Ray(P17, C17) → sr17
  117. Intersect(rt1, sr17) → F17
  118. Rotate(F17, (16 * θ), P0) → W17
  119. Circle(P0, F17) → c17
  120. If(x(F17) < x(P0), 1, 2) → SnDx17
  121. Intersect(c17, rt0, SnDx17) → P18
  122. Rotate(B18, α + (17 * γ), P18) → C18
  123. Ray(P18, C18) → sr18
  124. Intersect(rt1, sr18) → F18
  125. Rotate(F18, (17 * θ), P0) → W18
  126. If(x(F18) < x(P0), 1, 2) → SnDx18
  127. Circle(P0, F18) → c18
  128. Intersect(c18, rt0, SnDx18) → P19
  129. Rotate(B19, α + (18 * γ), P19) → C19
  130. Ray(P19, C19) → sr19
  131. Intersect(rt1, sr19) → F19
  132. Rotate(F19, (18 * θ), P0) → W19
  133. Circle(P0, F19) → c19
  134. If(x(F19) < x(P0), 1, 2) → SnDx19
  135. Intersect(c19, rt0, SnDx19) → P20
  136. Rotate(B20, α + (19 * γ), P20) → C20
  137. Ray(P20, C20) → sr20
  138. Intersect(rt1, sr20) → F20
  139. Rotate(F20, (19 * θ), P0) → W20
  140. If(x(F20) < x(P0), 1, 2) → SnDx20
  141. Circle(P0, F20) → c20
  142. Intersect(c20, rt0, SnDx20) → P21
  143. Rotate(B21, α + (20 * γ), P21) → C21
  144. Ray(P21, C21) → sr21
  145. Intersect(rt1, sr21) → F21
  146. Rotate(F21, (20 * θ), P0) → W21
  147. Circle(P0, F21) → c21
  148. If(x(F21) < x(P0), 1, 2) → SnDx21
  149. Intersect(c21, rt0, SnDx21) → P22
  150. Rotate(B22, α + (21 * γ), P22) → C22
  151. Ray(P22, C22) → sr22
  152. Intersect(rt1, sr22) → F22
  153. Rotate(F22, (21 * θ), P0) → W22
  154. If(x(F22) < x(P0), 1, 2) → SnDx22
  155. Circle(P0, F22) → c22
  156. Intersect(c22, rt0, SnDx22) → P23
  157. Rotate(B23, α + (22 * γ), P23) → C23
  158. Ray(P23, C23) → sr23
  159. Intersect(rt1, sr23) → F23
  160. Rotate(F23, (22 * θ), P0) → W23
  161. Circle(P0, F23) → c23
  162. If(x(F23) < x(P0), 1, 2) → SnDx23
  163. Intersect(c23, rt0, SnDx23) → P24
  164. Rotate(B24, α + (23 * γ), P24) → C24
  165. Ray(P24, C24) → sr24
  166. Intersect(rt1, sr24) → F24
  167. Rotate(F24, (23 * θ), P0) → W24
  168. If(x(F24) < x(P0), 1, 2) → SnDx24
  169. Circle(P0, F24) → c24
  170. Intersect(c24, rt0, SnDx24) → P25
  171. Rotate(B25, α + (24 * γ), P25) → C25
  172. Ray(P25, C25) → sr25
  173. Intersect(rt1, sr25) → F25
  174. Rotate(F25, (24 * θ), P0) → W25
  175. Circle(P0, F25) → c25
  176. If(x(F25) < x(P0), 1, 2) → SnDx25
  177. Intersect(c25, rt0, SnDx25) → P26
  178. Rotate(B26, α + (25 * γ), P26) → C26
  179. Ray(P26, C26) → sr26
  180. Intersect(rt1, sr26) → F26
  181. Rotate(F26, (25 * θ), P0) → W26
  182. If(x(F26) < x(P0), 1, 2) → SnDx26
  183. Circle(P0, F26) → c26
  184. Intersect(c26, rt0, SnDx26) → P27
  185. Rotate(B27, α + (26 * γ), P27) → C27
  186. Ray(P27, C27) → sr27
  187. Intersect(rt1, sr27) → F27
  188. Rotate(F27, (26 * θ), P0) → W27
  189. Circle(P0, F27) → c27
  190. If(x(F27) < x(P0), 1, 2) → SnDx27
  191. Intersect(c27, rt0, SnDx27) → P28
  192. Rotate(B28, α + (27 * γ), P28) → C28
  193. Ray(P28, C28) → sr28
  194. Intersect(rt1, sr28) → F28
  195. Rotate(F28, (27 * θ), P0) → W28
  196. If(x(F28) < x(P0), 1, 2) → SnDx28
  197. Circle(P0, F28) → c28
  198. Intersect(c28, rt0, SnDx28) → P29
  199. Rotate(B29, α + (28 * γ), P29) → C29
  200. Ray(P29, C29) → sr29
  201. Intersect(rt1, sr29) → F29
  202. Rotate(F29, (28 * θ), P0) → W29
  203. Circle(P0, F29) → c29
  204. If(x(F29) < x(P0), 1, 2) → SnDx29
  205. Intersect(c29, rt0, SnDx29) → P30
  206. Rotate(B30, α + (29 * γ), P30) → C30
  207. Ray(P30, C30) → sr30
  208. Intersect(rt1, sr30) → F30
  209. Rotate(F30, (29 * θ), P0) → W30
  210. If(x(F30) < x(P0), 1, 2) → SnDx30
  211. Circle(P0, F30) → c30
  212. Intersect(c30, rt0, SnDx30) → P31
  213. Rotate(B31, α + (30 * γ), P31) → C31
  214. Ray(P31, C31) → sr31
  215. Intersect(rt1, sr31) → F31
  216. Rotate(F31, (30 * θ), P0) → W31
  217. Circle(P0, F31) → c31
  218. If(x(F31) < x(P0), 1, 2) → SnDx31
  219. Intersect(c31, rt0, SnDx31) → P32
  220. Rotate(B32, α + (31 * γ), P32) → C32
  221. Ray(P32, C32) → sr32
  222. Intersect(rt1, sr32) → F32
  223. Rotate(F32, (31 * θ), P0) → W32
  224. If(x(F32) < x(P0), 1, 2) → SnDx32
  225. Circle(P0, F32) → c32
  226. Intersect(c32, rt0, SnDx32) → P33
  227. Rotate(B33, α + (32 * γ), P33) → C33
  228. Ray(P33, C33) → sr33
  229. Intersect(rt1, sr33) → F33
  230. Rotate(F33, (32 * θ), P0) → W33
  231. Circle(P0, F33) → c33
  232. If(x(F33) < x(P0), 1, 2) → SnDx33
  233. Intersect(c33, rt0, SnDx33) → P34
  234. Rotate(B34, α + (33 * γ), P34) → C34
  235. Ray(P34, C34) → sr34
  236. Intersect(rt1, sr34) → F34
  237. Rotate(F34, (33 * θ), P0) → W34
  238. If(x(F34) < x(P0), 1, 2) → SnDx34
  239. Circle(P0, F34) → c34
  240. Intersect(c34, rt0, SnDx34) → P35
  241. Rotate(B35, α + (34 * γ), P35) → C35
  242. Ray(P35, C35) → sr35
  243. Intersect(rt1, sr35) → F35
  244. Rotate(F35, (34 * θ), P0) → W35
  245. Circle(P0, F35) → c35
  246. If(x(F35) < x(P0), 1, 2) → SnDx35
  247. Intersect(c35, rt0, SnDx35) → P36
  248. Rotate(B36, α + (35 * γ), P36) → C36
  249. Ray(P36, C36) → sr36
  250. Intersect(rt1, sr36) → F36
  251. Rotate(F36, (35 * θ), P0) → W36
  252. Circle(P0, F36) → c36
  253. If(x(F36) < x(P0), 1, 2) → SnDx36
  254. Intersect(c36, rt0, SnDx36) → P37
  255. Max(RemoveUndefined[{MxP1, MxP2, MxP3, MxP4, MxP5, MxP6, MxP7, MxP8, MxP9, MxP10, MxP11, MxP12, MxP13, MxP14, MxP15, MxP16, MxP17, MxP18, MxP19, MxP20, MxP21, MxP22, MxP23, MxP24, MxP25, MxP26, MxP27, MxP28, MxP29, MxP30, MxP31, MxP32, MxP33, MxP34, MxP35, MxP36, MxP37}]) → QuadMaxX
  256. Segment(P1, F1) → sp1
  257. Segment(P2, F2) → g_2
  258. Segment(P3, F3) → i_2
  259. Segment(P4, F4) → k_2
  260. Circle(P0, P1) → c0
  261. Segment(P5, F5) → m_2
  262. Segment(P6, F6) → r_2
  263. Segment(P7, F7) → a_2
  264. Segment(P8, F8) → f_3
  265. Segment(P9, F9) → h_3
  266. Segment(P10, F10) → j_3
  267. Segment(P11, F11) → m_3
  268. Segment(P12, F12) → q_3
  269. Segment(P13, F13) → t_3
  270. Segment(P14, F14) → b_3
  271. Segment(P15, F15) → g_4
  272. Segment(P16, F16) → i_4
  273. Segment(P17, F17) → l_4
  274. Segment(P18, F18) → n_4
  275. Segment(P19, F19) → s_4
  276. Segment(P20, F20) → b_4
  277. Segment(P21, F21) → g_5
  278. Segment(P22, F22) → i_5
  279. Segment(P23, F23) → k_5
  280. Segment(P24, F24) → m_5
  281. Segment(P25, F25) → r_5
  282. Segment(P26, F26) → a_5
  283. Segment(P27, F27) → f_6
  284. Segment(P28, F28) → h_6
  285. Segment(P29, F29) → j_6
  286. Segment(P30, F30) → m_6
  287. Segment(P31, F31) → q_6
  288. Segment(P32, F32) → t_6
  289. Segment(P33, F33) → b_6
  290. Segment(P34, F34) → g_7
  291. Segment(P35, F35) → i_7
  292. Segment(P36, F36) → l_7
  293. Segment(P1, F1) → m_7
  294. Segment(F1, W2) → sp2
  295. Segment(W2, W3) → sp3
  296. Segment(W3, W4) → sp4
  297. Segment(W4, W5) → sp5
  298. Segment(W5, W6) → sp6
  299. Segment(W6, W7) → sp7
  300. Segment(W7, W8) → sp8
  301. Segment(W8, W9) → sp9
  302. Segment(W9, W10) → sp10
  303. Segment(W10, W11) → sp11
  304. Segment(W11, W12) → sp12
  305. Segment(W12, W13) → sp13
  306. Segment(W13, W14) → sp14
  307. Segment(W14, W15) → sp15
  308. Segment(W15, W16) → sp16
  309. Segment(W16, W17) → sp17
  310. Segment(W17, W18) → sp18
  311. Segment(W18, W19) → sp19
  312. Segment(W19, W20) → sp20
  313. Segment(W20, W21) → sp21
  314. Segment(W21, W22) → sp22
  315. Segment(W22, W23) → sp23
  316. Segment(W23, W24) → sp24
  317. Segment(W24, W25) → sp25
  318. Segment(W25, W26) → sp26
  319. Segment(W26, W27) → sp27
  320. Segment(W27, W28) → sp28
  321. Segment(W28, W29) → sp29
  322. Segment(W29, W30) → sp30
  323. Segment(W30, W31) → sp31
  324. Segment(W31, W32) → sp32
  325. Segment(W32, W33) → sp33
  326. Segment(W33, W34) → sp34
  327. Segment(W34, W35) → sp35
  328. Segment(W35, W36) → sp36
  329. Segment(P0, W2) → sg2
  330. Segment(P0, W3) → sg3
  331. Segment(P0, W4) → sg4
  332. Segment(P0, W5) → sg5
  333. Segment(P0, W6) → sg6
  334. Segment(P0, W7) → sg7
  335. Segment(P0, W8) → sg8
  336. Segment(P0, W9) → sg9
  337. Segment(P0, W10) → sg10
  338. Segment(P0, W11) → sg11
  339. Segment(P0, W12) → sg12
  340. Segment(P0, W13) → sg13
  341. Segment(P0, W14) → sg14
  342. Segment(P0, W15) → sg15
  343. Segment(P0, W16) → sg16
  344. Segment(P0, W17) → sg17
  345. Segment(P0, W18) → sg18
  346. Segment(P0, W19) → sg19
  347. Segment(P0, W20) → sg20
  348. Segment(P0, W21) → sg21
  349. Segment(P0, W22) → sg22
  350. Segment(P0, W23) → sg23
  351. Segment(P0, W24) → sg24
  352. Segment(P0, W25) → sg25
  353. Segment(P0, W26) → sg26
  354. Segment(P0, W27) → sg27
  355. Segment(P0, W28) → sg28
  356. Segment(P0, W29) → sg29
  357. Segment(P0, W30) → sg30
  358. Segment(P0, W31) → sg31
  359. Segment(P0, W32) → sg32
  360. Segment(P0, W33) → sg33
  361. Segment(P0, W34) → sg34
  362. Segment(P0, W35) → sg35
  363. Segment(P0, W36) → sg36
  364. Textfield(CN) → CampoInserimento1
  365. Segment(PS, PD) → sg0
  366. Rotate(PS, θ) → AS
  367. Rotate(PD, θ) → AD
  368. Segment(AS, AD) → sg1
  369. Last(RemoveUndefined[{W1, W2, W3, W4, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15, W16, W17, W18, W19, W20, W21, W22, W23, W24, W25, W26, W27, W28, W29, W30, W31, W32, W33, W34, W35, W36}]) → AAA
  370. Midpoint(sp1) → Pm1
  371. Midpoint(sp2) → Pm2
  372. OrthogonalLine(Pm1, sp1) → perp1
  373. OrthogonalLine(Pm2, sp2) → perp2
  374. Intersect(perp1, perp2) → CeCe
  375. Circle(CeCe, P1) → cerchietto

AI Drawing Prompt Reference

Draw a line segment that can be adjusted for angle and inclination. Start by drawing a line segment rt0 through point P0 and point A. Then, rotate point A around point P0 to get point A1, and draw a new line segment rt1 through P0 and A1. Next, rotate point B1 around point P1 to get point C1, and draw a ray sr1 through P1 and C1. The line segment rt1 and the ray sr1 intersect at point F1. Repeat this process by rotating and intersecting to gradually adjust the direction and position of the line segment, ultimately resulting in multiple rotated line segments and points.
The prompt above was compiled from the original drawing commands and is for reference only.