Transformations Game

Transformations Game
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2020-02-04 21:36
This example uses a game format to demonstrate geometric transformations, including translation, reflection, and rotation. It involves core mathematical concepts from coordinate geometry. Using GeoGebra commands such as Point, Rotate, and Mirror, dynamic geometric figures can be constructed. Suitable for middle school and above students to learn about transformations and related concepts.

GeoGebra Commands & Parameters

  1. Point(yAxis) → C
  2. Circle(C, D) → c
  3. Point(c) → Rotate
  4. Rotate(Rotate, 120*°, C) → E'
  5. Rotate(Rotate, 90*°, C) → E'_1
  6. Mirror(Rotate, C) → E'_2
  7. Mirror(E'_1, C) → V_1
  8. Point(c) → C_2
  9. CircleArc(C, C_2, Rotate) → d
  10. Angle(C_2, C, Rotate) → α
  11. Point(c) → U_2
  12. Rotate(U_2, 90*°, C) → V_2
  13. Rotate(U_2, -90*°, C) → W_2
  14. LaTeX(right, true, true) → text5
  15. Textfield(B1) → inputBox1
  16. Element(list1, a) → β
  17. Polygon(J, K, L) → poly1, l, j, k
  18. Polygon(J', K', L') → poly2, l_1, j_1, k_1
  19. Rotate(J, 90*°, C) → J'_3
  20. Rotate(K, 90*°, C) → K'_3
  21. Rotate(L, 90*°, C) → L'_3
  22. Polygon(J'_3, K'_3, L'_3) → poly1', l', j', k'
  23. Rotate(J, 180*°, C) → J'_1
  24. Rotate(K, 180*°, C) → K'_1
  25. Rotate(L, 180*°, C) → L'_1
  26. Polygon(J'_1, K'_1, L'_1) → poly1'_1, l'_1, j'_1, k'_1
  27. Rotate(J, -90*°, C) → J'_2
  28. Rotate(K, -90*°, C) → K'_2
  29. Rotate(L, -90*°, C) → L'_2
  30. Polygon(J'_2, K'_2, L'_2) → poly1'_2, l'_2, j'_2, k'_2
  31. Circle(C, K) → p
  32. Circle(C, L) → q
  33. Circle(C, J) → r
  34. Rotate(K, γ, C) → K'_4
  35. Angle(K, C, K'_4) → δ
  36. Rotate(L, γ, C) → L'_4
  37. Angle(L, C, L'_4) → ε
  38. Rotate(J, γ, C) → J'_4
  39. Angle(J, C, J'_4) → ζ
  40. Polygon(L'_4, K'_4, J'_4) → poly3, j'_4, l'_4, k'_4
  41. Mirror(K, xAxis) → K'_5
  42. Mirror(J, xAxis) → J'_5
  43. Mirror(L, xAxis) → L'_5
  44. Mirror(K, yAxis) → K'_6
  45. Mirror(J, yAxis) → J'_6
  46. Mirror(L, yAxis) → L'_6
  47. Midpoint(J, J'_5) → J_1
  48. Midpoint(K, K'_5) → K_1
  49. Midpoint(L, L'_5) → E_3
  50. Circle(K_1, K) → s
  51. Circle(J_1, J) → t
  52. Circle(E_3, L) → c_1
  53. Rotate(K, η, K_1) → K'_7
  54. Angle(K, K_1, K'_7) → θ
  55. Rotate(J, η, J_1) → J'_7
  56. Angle(J, J_1, J'_7) → ι
  57. Rotate(L, η, E_3) → L'_7
  58. Angle(L, E_3, L'_7) → κ
  59. Segment(K, K'_5) → m
  60. Segment(J, J'_5) → n
  61. Segment(L, L'_5) → a_1
  62. Line(K'_7, xAxis) → b_1
  63. Line(J'_7, xAxis) → d_1
  64. Line(L'_7, xAxis) → e_1
  65. Intersect(b_1, m) → F_3
  66. Intersect(n, d_1) → G_3
  67. Intersect(a_1, e_1) → H_3
  68. Polygon(F_3, G_3, H_3) → poly4, h_3, f_3, g_3
  69. Midpoint(K'_6, K) → I_3
  70. Circle(I_3, K) → f_1
  71. Rotate(K, η, I_3) → K'_8
  72. Angle(K, I_3, K'_8) → λ
  73. Segment(K'_6, K) → g_1
  74. Line(K'_8, yAxis) → h_1
  75. Intersect(h_1, g_1) → M_3
  76. Midpoint(J, J'_6) → N_3
  77. Circle(N_3, J) → p_1
  78. Rotate(J, η, N_3) → J'_8
  79. Angle(J, N_3, J'_8) → μ
  80. Segment(J'_6, J) → i_1
  81. Line(J'_8, yAxis) → m_1
  82. Intersect(i_1, m_1) → O_3
  83. Midpoint(L'_6, L) → P_3
  84. Circle(P_3, L) → q_1
  85. Rotate(L, η, P_3) → L'_8
  86. Angle(L, P_3, L'_8) → ν
  87. Segment(L'_6, L) → n_1
  88. Line(L'_8, yAxis) → r_1
  89. Intersect(r_1, n_1) → Q_3
  90. Polygon(Q_3, M_3, O_3) → poly5, o_3, q_3, m_3
  91. LaTeX(wrong, true, true) → text11
  92. Point(xAxis) → L_1
  93. Mirror(pic1, xAxis) → pic1'
  94. Mirror(pic1', xAxis) → pic1''
  95. Rotate(pic1'', 90*°, C) → pic1'''
  96. Rotate(pic1', 90*°, C) → pic1''_1
  97. Textfield(Date) → inputBox2
  98. Textfield(Name) → inputBox3

AI Drawing Prompt Reference

Draw a coordinate system with a point on the y-axis, create a circle centered at this point, and take a point on the circle. Rotate this point by 120 degrees and 90 degrees around the center to get two new points. Reflect these points across the center to get two more points. Connect the original point on the circle to the rotated points with line segments, and label the angles and lengths of the segments.
The prompt above was compiled from the original drawing commands and is for reference only.