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Varying Quantities of Red and Blue Paint on a Line

Varying Quantities of Red and Blue Paint on a Line
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2020-01-14 22:34
Coordinate GeometryMatrixTransformationSlider AnimationGraphing
In collections The variable-parts perspective across the curriculum
This GeoGebra example dynamically illustrates how varying quantities of red and blue paint relate along a straight line, using sliders or moving points to show proportional changes and total amounts. The core mathematical concepts include linear relationships, ratios, coordinate geometry, and geometric transformations such as scaling or translation via matrices. The construction employs commands like Point, Line, OrthogonalLine, Circle, Intersect, Polygon, Segment, and Ray to build base elements, with a slider (e.g., 'size') controlling variables, resulting in scatter plots or pyramid-like visual structures. It is suitable for middle and high school students learning linear functions, proportions, and transformations, as well as for teachers demonstrating dynamic mathematical modeling.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Line(A, B) → a
  4. OrthogonalLine(A, a) → b
  5. Circle(A, 0.7) → c
  6. Intersect(c, a, 1) → C
  7. Intersect(c, b, 1) → D
  8. Circle(D, 0.5) → d
  9. Circle(C, 0.5) → e
  10. Intersect(e, a, 1) → E
  11. Intersect(d, b, 1) → F
  12. Line(D, a) → f
  13. Line(F, f) → g
  14. Line(C, b) → h
  15. Line(E, b) → i
  16. Circle(F, size) → k
  17. Intersect(k, g, 2) → G
  18. Circle(G, size) → p
  19. Intersect(p, g, 2) → H
  20. Circle(H, size) → q
  21. Intersect(q, g, 2) → I
  22. Circle(I, size) → r
  23. Intersect(r, g, 2) → J
  24. Circle(J, size) → s
  25. Intersect(s, g, 2) → K
  26. Intersect(a, i) → L
  27. Circle(E, size) → t
  28. Intersect(t, i, 2) → M
  29. Circle(M, size) → c_1
  30. Intersect(c_1, i, 2) → N
  31. Circle(N, size) → d_1
  32. Intersect(d_1, i, 2) → O
  33. OrthogonalLine(G, g) → j
  34. OrthogonalLine(H, g) → l
  35. OrthogonalLine(I, g) → m
  36. OrthogonalLine(J, g) → n
  37. OrthogonalLine(K, g) → a_1
  38. OrthogonalLine(M, i) → b_1
  39. OrthogonalLine(N, i) → e_1
  40. OrthogonalLine(O, i) → f_1
  41. Intersect(a_1, f_1) → P
  42. Intersect(a_1, f_1) → Q
  43. Intersect(h, f_1) → R
  44. Intersect(h, e_1) → S
  45. Intersect(h, b_1) → T
  46. Intersect(f, j) → U
  47. Intersect(f, l) → V
  48. Intersect(f, m) → W
  49. Intersect(f, n) → Z
  50. Intersect(f, a_1) → A_1
  51. Polygon(D, F, G, U) → poly1, d_2, f_2, g_1, u
  52. Polygon(U, G, H, V) → poly2, u_1, g_2, h_1, v
  53. Polygon(H, I, W, V) → poly3, h_2, i_1, w, v_1
  54. Polygon(E, C, T, M) → poly6, e_2, c_2, t_1, m_1
  55. Polygon(T, S, N, M) → poly7, t_2, s_1, n_1, m_2
  56. Polygon(S, R, O, N) → poly8, s_2, r_1, o, n_2
  57. Circle(F, 0.3) → p_1
  58. Circle(K, 0.3) → q_1
  59. Circle(O, 0.3) → k_2
  60. Circle(E, 0.3) → p_2
  61. Intersect(k_2, f_1, 2) → B_1
  62. Intersect(p_2, a, 1) → C_1
  63. Intersect(p_1, b, 1) → D_1
  64. Intersect(q_1, a_1, 1) → E_1
  65. Intersect(x = 5, y = 3) → F_1
  66. Circle(O, size) → k_1
  67. Intersect(k_1, i, 2) → G_1
  68. OrthogonalLine(G_1, i) → j_1
  69. Intersect(h, j_1) → H_1
  70. Polygon(O, R, H_1, G_1) → poly4, o_1, r_2, h_3, g_3
  71. Circle(G_1, 0.3) → q_2
  72. Intersect(q_2, j_1, 2) → I_1
  73. Circle(I, 0.3) → c_3
  74. Intersect(c_3, m, 1) → J_1
  75. Segment(D_1, J_1) → l_1
  76. Segment(I_1, C_1) → a_2
  77. Intersect(m, j_1) → K_1
  78. Intersect(x = 3, y = 4) → L_1
  79. Ray(A, L_1) → b_2
  80. Circle(J, 0.3) → d_3
  81. Intersect(d_3, n, 1) → M_1
  82. Segment(D_1, M_1) → i_2
  83. Segment(C_1, B_1) → j_2
  84. Polygon(W, I, J, Z) → poly5, w_1, i_3, j_3, z_1
  85. Intersect(n, f_1) → N_1
  86. Ray(A, N_1) → l_2

AI Drawing Prompt Reference

Draw a straight line and mark two points on it. Create two circles with different radii centered at these points, and find their intersections with the line. Construct additional circles and lines using these intersection points to form a complex geometric pattern. Use a slider to control the size of some circles, showing dynamic changes. The overall design should illustrate linear relationships and proportional changes, suitable for educational purposes.
The prompt above was compiled from the original drawing commands and is for reference only.