MathPlotAI Logo MathPlotAI

Rotations, Reflections, and Translations of a Triangle

Rotations, Reflections, and Translations of a Triangle
Loading the math board and drawing, please wait…
2014-02-22 21:38
PolygonVectorTransformationGeometric Construction
In collections MalinC's GeoGebra-book
This example demonstrates a triangle being rotated four times, then reflected across the y-axis, and finally translated along a vector. Key mathematical concepts include rotation, reflection, and translation. Using GeoGebra commands such as Polygon, Rotate, Mirror, Vector, and Translate, the geometric transformations are visually illustrated. Suitable for students at the middle school level and above to learn about geometric transformations and the patterns of figure transformations.

GeoGebra Commands & Parameters

  1. Polygon(A1, B1, C1) → D1, E1, F1, G1
  2. Rotate(A1, 72°) → A2
  3. Rotate(B1, 72°) → B2
  4. Rotate(C1, 72°) → C2
  5. Polygon(A2, B2, C2) → D2, E2, F2, G2
  6. Rotate(A2, 72°) → A3
  7. Rotate(B2, 72°) → B3
  8. Rotate(C2, 72°) → C3
  9. Polygon(A3, B3, C3) → D3, E3, F3, G3
  10. Rotate(A3, 72°) → A4
  11. Rotate(B3, 72°) → B4
  12. Rotate(C3, 72°) → C4
  13. Polygon(A4, B4, C4) → D4, E4, F4, G4
  14. Rotate(A4, 72°) → A5
  15. Rotate(B4, 72°) → B5
  16. Rotate(C4, 72°) → C5
  17. Polygon(A5, B5, C5) → D5, E5, F5, G5
  18. Mirror(A1, yAxis) → A6
  19. Mirror(B1, yAxis) → B6
  20. Mirror(C1, yAxis) → C6
  21. Polygon(A6, B6, C6) → D6, E6, F6, G6
  22. Mirror(A2, yAxis) → A7
  23. Mirror(B2, yAxis) → B7
  24. Mirror(C2, yAxis) → C7
  25. Mirror(A3, yAxis) → A8
  26. Mirror(B3, yAxis) → B8
  27. Mirror(C3, yAxis) → C8
  28. Mirror(A4, yAxis) → A9
  29. Mirror(B4, yAxis) → B9
  30. Mirror(C4, yAxis) → C9
  31. Mirror(A5, yAxis) → A10
  32. Mirror(B5, yAxis) → B10
  33. Mirror(C5, yAxis) → C10
  34. Polygon(A7, B7, C7) → D7, E7, F7, G7
  35. Polygon(A8, B8, C8) → D8, E8, F8, G8
  36. Polygon(A9, B9, C9) → D9, E9, F9, G9
  37. Vector(A, B) → u
  38. Translate(A1, u) → A11
  39. Translate(B1, u) → B11
  40. Translate(C1, u) → C11
  41. Translate(A2, u) → A12
  42. Translate(B2, u) → B12
  43. Translate(C2, u) → C12
  44. Translate(A3, u) → A13
  45. Translate(B3, u) → B13
  46. Translate(C3, u) → C13
  47. Translate(A4, u) → A14
  48. Translate(B4, u) → B14
  49. Translate(C4, u) → C14
  50. Translate(A5, u) → A15
  51. Translate(B5, u) → B15
  52. Translate(C5, u) → C15
  53. Translate(A6, u) → A16
  54. Translate(B6, u) → B16
  55. Translate(C6, u) → C16
  56. Translate(A7, u) → A17
  57. Translate(B7, u) → B17
  58. Translate(C7, u) → C17
  59. Translate(A8, u) → A18
  60. Translate(B8, u) → B18
  61. Translate(C8, u) → C18
  62. Translate(A9, u) → A19
  63. Translate(B9, u) → B19
  64. Translate(C9, u) → C19
  65. Translate(A10, u) → A20
  66. Translate(B10, u) → B20
  67. Translate(C10, u) → C20
  68. Polygon(A10, B10, C10) → D10, E10, F10, G10
  69. Polygon(A11, B11, C11) → D11, E11, F11, G11
  70. Polygon(A12, B12, C12) → D12, E12, F12, G12
  71. Polygon(A13, B13, C13) → D13, E13, F13, G13
  72. Polygon(A14, B14, C14) → D14, E14, F14, G14
  73. Polygon(A15, B15, C15) → D15, E15, F15, G15
  74. Polygon(A16, B16, C16) → D16, E16, F16, G16
  75. Polygon(A17, B17, C17) → D17, E17, F17, G17
  76. Polygon(A18, B18, C18) → D18, E18, F18, G18
  77. Polygon(A19, B19, C19) → D19, E19, F19, G19
  78. Polygon(A20, B20, C20) → D20, E20, F20, G20

AI Drawing Prompt Reference

Draw a triangle, then rotate it four times by 72 degrees each time, reflect each resulting triangle across the y-axis, and translate each triangle along vector u. Finally, draw all the generated triangles.
The prompt above was compiled from the original drawing commands and is for reference only.