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Visualizing Systems of Linear Equations

Visualizing Systems of Linear Equations
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2012-05-07 20:21
VectorCoordinate GeometryGeometric ConstructionGraphing
This example dynamically demonstrates the solution set of a system of linear equations, intuitively showing the geometric meaning of the equations. It involves core math concepts like linear equations, vectors, coordinate geometry, and geometric construction. GeoGebra commands used include Intersect (intersection), Line (line), Vector (vector), Mirror (reflection), and Segment (segment). Suitable for high school mathematics teaching to help students understand the solution methods and geometric representation of linear equations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Line(A, K) → c
  3. Vector(A, B) → u
  4. Mirror(A, B) → A'_1
  5. Mirror(A, B) → A'_2
  6. Vector(A, A'_2) → v
  7. Mirror(B, A'_2) → B'_1
  8. Vector(A, B'_1) → w
  9. Mirror(B, A) → B'_2
  10. Mirror(A, B'_2) → A'_3
  11. Vector(A, B'_2) → z
  12. Vector(A, A'_3) → d
  13. Vector(A, C) → e
  14. Mirror(A, C) → A'_4
  15. Mirror(C, A'_4) → C'_1
  16. Vector(A, A'_4) → f
  17. Vector(A, C'_1) → g
  18. Mirror(C, A) → C'_2
  19. Mirror(A, C'_2) → A'_5
  20. Vector(A, C'_2) → h
  21. Vector(A, A'_5) → i
  22. Line(C, u) → j
  23. Line(C, u) → k
  24. Line(C, u) → l
  25. Line(B, e) → m
  26. Intersect(j, m) → D
  27. Mirror(A, D) → A'_6
  28. Vector(A, D) → n
  29. Segment(B, D) → p
  30. Segment(C, D) → q
  31. Vector(A, A'_6) → r
  32. Segment(A'_2, A'_6) → s
  33. Segment(A'_4, A'_6) → t
  34. Mirror(D, A'_6) → D'_1
  35. Vector(A, D'_1) → u_1
  36. Segment(C'_1, D'_1) → a_1
  37. Segment(D'_1, B'_1) → b_1
  38. Mirror(D, A) → D'_2
  39. Mirror(A, D'_2) → A'
  40. Vector(A, D'_2) → v_1
  41. Segment(C'_2, D'_2) → c_1
  42. Segment(D'_2, B'_2) → d_1
  43. Vector(A, A') → w_1
  44. Segment(A'_3, A') → e_1
  45. Segment(A'_5, A') → f_1
  46. Vector(A, E) → z_1
  47. Mirror(B, D) → B'_3
  48. Vector(A, B'_3) → g_1
  49. Segment(B, B'_3) → h_1
  50. Segment(B'_3, A'_4) → i_1
  51. Mirror(D, B'_3) → D'_3
  52. Segment(C'_1, D'_3) → j_1
  53. Segment(B, D'_3) → k_1
  54. Vector(A, D'_3) → l_1
  55. Vector(A, C) → m_1
  56. Vector(A, B) → n_1
  57. Mirror(D, B) → D'_4
  58. Vector(A, D'_4) → p_1
  59. Segment(C'_2, D'_4) → q_1
  60. Segment(D'_4, B) → r_1
  61. Mirror(B, D'_4) → B'
  62. Segment(A'_5, B') → s_1
  63. Segment(B', B) → t_1
  64. Vector(A, B') → u_2
  65. Mirror(C, D) → C'_3
  66. Vector(A, C'_3) → v_2
  67. Segment(C, C'_3) → a_2
  68. Segment(C'_3, A'_2) → b_2
  69. Mirror(C'_3, A'_6) → C''_1
  70. Vector(A, C''_1) → w_2
  71. Segment(A'_2, C''_1) → c_2
  72. Segment(C''_1, C'_1) → d_2
  73. Mirror(C'_2, D'_4) → F
  74. Segment(C'_2, F) → e_2
  75. Segment(A'_2, F) → f_2
  76. Vector(A, F) → z_2
  77. Mirror(A'_5, B') → G
  78. Vector(A, G) → g_2
  79. Segment(A'_5, G) → h_2
  80. Segment(G, A'_2) → i_2
  81. Mirror(B', G) → B''
  82. Segment(A'_5, B'') → j_2
  83. Segment(B'', B'_1) → k_2
  84. Vector(A, B'') → l_2
  85. Mirror(D'_4, F) → D''
  86. Vector(A, D'') → m_2
  87. Segment(C'_2, D'') → n_2
  88. Segment(D'', B'_1) → p_2
  89. Mirror(D, C'_3) → D'
  90. Segment(C, D') → q_2
  91. Segment(B'_1, D') → r_2
  92. Vector(A, D') → s_2
  93. Mirror(B'_3, A'_6) → H
  94. Vector(A, H) → t_2
  95. Segment(A'_4, H) → a_3
  96. Segment(B'_1, H) → b_3
  97. Vector(A, B'_1) → u_3
  98. Vector(A, A'_2) → v_3
  99. Vector(A, B'_2) → w_3
  100. Vector(A, A'_3) → z_3
  101. Vector(A, A'_5) → c_3
  102. Vector(A, C'_2) → d_3
  103. Vector(A, A'_4) → e_3
  104. Vector(A, C'_1) → f_3
  105. Mirror(D'_4, A) → I
  106. Vector(A, I) → g_3
  107. Segment(C, I) → h_3
  108. Segment(B'_2, I) → i_3
  109. Mirror(I, E) → I'
  110. Segment(I', C'_1) → j_3
  111. Segment(I', B'_2) → k_3
  112. Vector(A, I') → l_3
  113. Mirror(B'_2, D'_2) → J
  114. Vector(A, J) → m_3
  115. Segment(B'_2, J) → n_3
  116. Segment(J, A'_5) → p_3
  117. Mirror(C'_2, D'_2) → L
  118. Segment(A'_3, L) → q_3
  119. Segment(L, C'_2) → r_3
  120. Vector(A, L) → s_3
  121. Mirror(C, I) → C'
  122. Vector(A, C') → t_3
  123. Segment(C, C') → a_4
  124. Segment(A'_3, C') → b_4
  125. Mirror(A'_3, C') → M
  126. Segment(A'_3, M) → c_4
  127. Segment(M, A'_4) → d_4
  128. Vector(A, M) → u_4
  129. Mirror(C', M) → C''
  130. Vector(A, C'') → v_4
  131. Segment(C'_1, C'') → e_4
  132. Segment(C'', A'_3) → f_4
  133. Segment(B'_2, E) → g_4
  134. Segment(E, A'_4) → h_4
  135. Vector(A, E) → w_4