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Animation: Triangle and Vector Transformations

Animation: Triangle and Vector Transformations
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2016-03-26 08:34
TriangleVectorTransformation
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Unit 5: Triangle Congruence
This example demonstrates the transformation of a triangle through various vector operations. Key mathematical concepts include triangles, vectors, and geometric transformations. Using GeoGebra commands such as Ray, Point, Angle, Circle, Intersect, Vector, Translate, Dilate, and Mirror, the example dynamically shows the rotation, translation, and scaling of a triangle. Suitable for middle school and above students to learn about geometric transformations and vectors.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. Ray(B, C) → b
  3. Ray(C, A) → c
  4. Point(a) → D_1
  5. Point(b) → E_1
  6. Point(c) → F_1
  7. Ray(A, F_1) → d
  8. Ray(B, D_1) → e
  9. Ray(C, E_1) → f
  10. Point(e) → D
  11. Point(f) → E
  12. Point(d) → F
  13. Angle(B, A, C) → α
  14. Angle(C, B, A) → β
  15. Angle(A, C, B) → γ
  16. Angle(F, A, B) → δ
  17. Angle(D, B, C) → ε
  18. Angle(E, C, A) → ζ
  19. Circle(A, 1.5) → g
  20. Circle(B, 1.5) → h
  21. Circle(C, 1.5) → k
  22. Intersect(g, c, 1) → G
  23. Intersect(g, a, 1) → H
  24. Intersect(g, c, 2) → I
  25. Intersect(h, b, 1) → J
  26. Intersect(h, a, 1) → K
  27. Intersect(h, a, 2) → L
  28. Intersect(k, b) → M, N
  29. Intersect(k, c) → O,
  30. CircleSector(A, H, G) → p
  31. CircleSector(B, J, K) → q
  32. CircleSector(C, O, M) → r
  33. CircleSector(C, N, O) → s
  34. CircleSector(B, L, J) → t
  35. CircleSector(A, I, H) → c_1
  36. Line(C, a) → i
  37. Vector(B, C) → u
  38. Vector(A, C) → v
  39. Translate(q, u) → q'
  40. Dilate(C, If[0 < j ≤ 1, j, 0], B) → C'
  41. Vector(B, C') → w
  42. Translate(q, w) → q'_1
  43. Mirror(q', C) → q''
  44. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], C) → C'_1
  45. Vector(A, C'_1) → m
  46. Translate(p, m) → p'
  47. Dilate(C, If[0 < n ≤ 1, n, 0], B) → C'_2
  48. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], C) → A'
  49. Vector(B, C'_2) → u_1
  50. Vector(A, A') → v_1
  51. If(0 < n ≤ 1, Translate[t, u_1], Translate[t, u]) → e_1
  52. If(1 < n ≤ 2, Translate[c_1, v_1], Translate[c_1, v]) → f_1
  53. Polygon(A, B, C) → poly1, c_2, a_2, b_1
  54. Line(A, B) → g_1
  55. Point(i) → P
  56. Point(i) → Q
  57. Angle(A, C, B) → η
  58. CircleSector(C, M, O) → p_1
  59. CircleSector(B, K, J) → q_1
  60. CircleSector(A, G, H) → r_1
  61. Translate(q_1, w) → s_1
  62. Translate(q_1, w) → t_1
  63. Vector(B, C) → w_1
  64. Translate(q_1, w_1) → e_2
  65. Rotate(e_2, 180°, C) → f_2
  66. Translate(r_1, m) → g_2
  67. CircleSector(C, O, N) → k_2
  68. CircleSector(B, J, L) → p_2
  69. CircleSector(A, H, I) → q_2
  70. Translate(p_2, u_1) → r_2
  71. Translate(p_2, u) → s_2
  72. Translate(q_2, v_1) → t_2
  73. Translate(q_1, u) → d_2
  74. Translate(q_1, w) → c_3
  75. Translate(A, w) → A'_1
  76. Translate(B, w) → B'
  77. Translate(C, w) → C'_3
  78. Polygon(A'_1, B', C'_3) → poly1', c'_3, a'_1, b'
  79. Translate(A, w_1) → A'_2
  80. Translate(B, w_1) → B'_1
  81. Translate(C, w_1) → C'_4
  82. Polygon(A'_2, B'_1, C'_4) → poly1'_1, c'_4, a'_2, b'_1
  83. Segment(C'_3, A'_1) → l
  84. Segment(A'_1, B') → l_1
  85. Segment(B', C'_3) → m_1
  86. Segment(C'_4, A'_2) → n_1
  87. Segment(A'_2, C'_3) → b_2
  88. Segment(C'_3, C'_4) → i_2
  89. Rotate(d_2, (((j - 1) * 180))°, C) → h_2
  90. Translate(r_1, m) → d_3
  91. Translate(A, m) → A'_3
  92. Translate(B, m) → B'_2
  93. Translate(C, m) → C'_5
  94. Polygon(A'_3, B'_2, C'_5) → poly1'_2, c'_5, a'_3, b'_2
  95. Segment(B'_2, C'_5) → i_1
  96. Segment(C'_5, A'_3) → j_1
  97. Segment(A'_3, B'_2) → k_1
  98. Line(A, C) → j_2
  99. Intersect(k, j_2) → R, S
  100. Rotate(S, (((j - 3) * 180))°, C) → S'
  101. CircleArc(C, S, S') → e_3
  102. Segment(A, B) → l_2
  103. Segment(B, C) → m_2
  104. Segment(A, C) → n_2
  105. Translate(q, w) → d_1
  106. Translate(q, u) → q'_2
  107. Rotate(q'_2, If[1 < j ≤ 2, (((-(j - 1)) * 180))°, 180°], C) → p''
  108. Translate(p, m) → p'_1
  109. Rotate(S, (((-(j - 3)) * 180))°, C) → S'_1
  110. CircleArc(C, S'_1, S) → f_3
  111. Ray(C, A) → a_3

AI Drawing Prompt Reference

Draw a triangle ABC and demonstrate its rotation, translation, and scaling through vector operations and geometric transformations. First, draw the three sides of the triangle, then generate three points D, E, and F through the sides. Next, draw the three interior angles α, β, and γ, as well as three circles with radii of 1.5 centered at the vertices. Use the intersection points of circles and sides to generate new points G, H, I, J, K, L, M, N, and O. Draw three arcs p, q, and r using these points. Then, perform translation and scaling transformations using vectors u and v to generate new arcs q', q'_1, and q''. Finally, complete the transformation display by mirroring and scaling operations to generate new points and vectors.
The prompt above was compiled from the original drawing commands and is for reference only.