积极 AI Logo 积极 AI

混合问题-加水问题的图形解法

混合问题-加水问题的图形解法
几何画板及绘图内容加载中，请稍等……
2015-03-12 19:14
解析几何几何作图函数图像
①本范例演示了通过图形方法解决混合问题中加水对浓度影响的计算与可视化；②涉及的核心数学概念包括比例、浓度计算、线性方程与图形表示；③作图要点提炼自构造摘要，使用了Line（直线）、Intersect（交点）、Segment（线段）、OrthogonalLine（垂线）、Midpoint（中点）等GeoGebra命令与对象；④适合初中及以上数学学习者，用于理解混合问题与图形结合的解题思路。

GeoGebra 命令及参数

  1. Line(B_4, A_4) → i
  2. Intersect(i, d) → C_4
  3. Textfield(m_11) → inputBoxm_11
  4. Textfield(m_21) → inputBoxm_21
  5. Textfield(w_11) → inputBoxw_11
  6. Textfield(m_32) → inputBoxm_32
  7. Line(A_1, C_1) → b
  8. Intersect(a, b) → B_1
  9. Segment(E_1, C_1) → b_1
  10. Segment(C_1, F_1) → c_1
  11. Segment(D_1, B_1) → a_1
  12. Segment(B_1, G_1) → d_1
  13. Segment(A_1, C_1) → g_1
  14. Line(A_2, C_2) → p
  15. OrthogonalLine(G_2, yAxis) → q
  16. Intersect(q, p) → B_2
  17. Segment(A_2, C_2) → g_2
  18. Segment(G_2, B_2) → d_2
  19. Segment(B_2, D_2) → a_2
  20. Segment(C_2, E_2) → b_2
  21. Line(A_3, B_3) → c
  22. Segment(C_2, F_2) → c_2
  23. Line(A_3, B_3) → f
  24. OrthogonalLine(F_3, yAxis) → g
  25. Intersect(g, f) → C_3
  26. Segment(G_3, B_3) → d_3
  27. Segment(D_3, B_3) → a_3
  28. Segment(E_3, C_3) → b_3
  29. Segment(C_3, F_3) → c_3
  30. Segment(G_4, B_4) → d_4
  31. Segment(B_4, D_4) → a_4
  32. Midpoint(D_2, E_2) → S_2
  33. Midpoint(D_3, E_3) → S_3
  34. Midpoint(D_4, E_4) → S_4
  35. Textfield(w_12) → inputBoxw_12
  36. Textfield(w_13) → inputBoxw_13
  37. Textfield(w_33) → inputBoxw_33
  38. Textfield(m_13) → inputBoxm_13
  39. Textfield(w_32) → inputBoxw_32
  40. Textfield(w_34) → inputBoxw_34
  41. Textfield(m_24) → inputBoxm_14
  42. Textfield(m_34) → inputBoxm_34
  43. Midpoint(D_1, E_1) → S_1
  44. Segment(F_4, C_4) → c_4
  45. Segment(E_4, C_4) → b_4
  46. VerticalText(Oy) → Oyv
  47. VerticalText(Oy2) → Oy2v
  48. Polygon(A, B, C, D) → poly1, a_5, b_5, c_5, d_5
  49. Vector(A, D) → u
  50. Translate(A, u) → A'
  51. Translate(B, u) → B'
  52. Translate(C, u) → C'
  53. Translate(D, u) → D'
  54. Polygon(A', B', C', D') → poly1', a', b', c', d'
  55. Translate(A, Vector[(2 * u)]) → A'_1
  56. Translate(B, Vector[(2 * u)]) → B'_1
  57. Translate(C, Vector[(2 * u)]) → C'_1
  58. Translate(D, Vector[(2 * u)]) → D'_1
  59. Polygon(A'_1, B'_1, C'_1, D'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1
  60. Point(a_5) → E
  61. Point(c'_1) → F
  62. Segment(E, F) → e
  63. Segment(A_3, C_3) → g_3
  64. Ray(F_3, C_3) → h
  65. Segment(A_4, C_4) → g_4
  66. Ray(E_4, C_4) → j