MathPlotAI Logo MathPlotAI

Square Transformation Demonstration

Square Transformation Demonstration
Loading the math board and drawing, please wait…
2016-12-22 22:06
VectorTransformationGeometric Construction
In collections CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates dynamic transformations of a square. Key mathematical concepts include geometric transformations, vectors, and loci. Using commands like Dilate, Polygon, and Rotate, users can dynamically modify the size and position of the square. Suitable for middle school and above students to learn about geometric transformations and vectors.

GeoGebra Commands & Parameters

  1. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], D) → A'
  2. Segment(A, A') → f
  3. Midpoint(f) → V
  4. OrthogonalLine(V, f) → j_2
  5. CircleArc(V, D, A) → k_2
  6. Intersect(k_2, j_2) → C_1,
  7. CircleArc(V, C_1, A) → q_2
  8. Polygon(A, D, 4) → poly1, a, b, c, d, C_2, D_2
  9. Rotate(A, If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], D) → C
  10. Rotate(A', If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], D) → A''
  11. Segment(C, A'') → f'
  12. Segment(A, D) → g
  13. Segment(D, C_2) → h
  14. Segment(C_2, D_2) → i
  15. Segment(D_2, A) → j
  16. Circle(C_2, (0.1 * j)) → k
  17. Circle(D, (0.1 * j)) → p
  18. Circle(A, (0.1 * j)) → q
  19. Circle(D_2, (0.1 * j)) → r
  20. Segment(A, C_2) → l
  21. Segment(D_2, D) → m
  22. Intersect(l, m) → E_1
  23. Intersect(r, j, 1) → F_1
  24. Intersect(r, m, 1) → G_1
  25. Intersect(r, i, 1) → H_1
  26. Intersect(k, i, 1) → I
  27. Intersect(k, l, 1) → J
  28. Intersect(k, h, 1) → K
  29. Intersect(p, h, 1) → L
  30. Intersect(p, m, 1) → M_1
  31. Intersect(p, g, 1) → N_1
  32. Intersect(q, g, 1) → O
  33. Intersect(q, l, 1) → P
  34. Intersect(q, j, 1) → Q
  35. Rotate(C, If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C_2) → R
  36. Rotate(A'', If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C_2) → A'''
  37. Segment(R, A''') → f''
  38. CircleSector(D, L, N_1) → s
  39. Rotate(R, If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D_2) → R'
  40. Rotate(A''', If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D_2) → S
  41. Segment(R', S) → f'''
  42. Dilate(D, If[4 < e ≤ 5, 5 - e, 0], C_2) → B'
  43. Vector(D, B') → u
  44. Translate(s, u) → s'
  45. Rotate(s', If[5 < e ≤ 6, ((e - 5) * π / 2), 1.5707963267948966], C_2) → s''
  46. Dilate(C_2, If[6 < e ≤ 7, 7 - e, 0], D_2) → C'
  47. Vector(C_2, C') → v
  48. Translate(s'', v) → s'''
  49. Rotate(s''', If[7 < e ≤ 8, ((e - 7) * π / 2), 1.5707963267948966], D_2) → t
  50. Dilate(D_2, If[8 < e ≤ 9, 9 - e, 0], A) → D'
  51. Vector(D_2, D') → w
  52. Translate(t, w) → t'
  53. Rotate(t', If[9 < e ≤ 10, ((e - 9) * π / 2), 1.5707963267948966], A) → t''
  54. Dilate(A, If[10 < e ≤ 11, 11 - e, 0], E_1) → A'_2
  55. Dilate(E_1, If[11 < e ≤ 12, 12 - e, 0], C_2) → E'
  56. Dilate(D_2, If[12 < e ≤ 13, 13 - e, 0], E_1) → D'_1
  57. Dilate(E_1, If[13 < e ≤ 14, 14 - e, 0], D) → E'_1
  58. Dilate(D_2, If[17 < e ≤ 18, 18 - e, 0], E_1) → D'_2
  59. Vector(D_2, D'_2) → u_1
  60. Rotate(E_1, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5707963267948966], E_1) → E'_2
  61. Rotate(E'_1, If[14 < e ≤ 15, ((e - 14) * π / 2), 1.5708], E_1) → T
  62. Rotate(E'_2, If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5707963267948966], E_1) → U
  63. Rotate(T, If[15 < e ≤ 16, ((e - 15) * π / 2), 1.5708], E_1) → T'
  64. Rotate(U, If[17 < e ≤ 18, ((e - 17) * π / 2), 1.5707963267948966], E_1) → U'
  65. Rotate(T', If[16 < e ≤ 17, ((e - 16) * π / 2), 1.5708], E_1) → T''
  66. Dilate(D, If[18 < e ≤ 19, 19 - e, 0], C_2) → B'_1
  67. Dilate(D, If[18 < e ≤ 19, 19 - e, 0], A) → B'_2
  68. Dilate(D, If[18 < e ≤ 19, 19 - e, 0], D_2) → B'_3
  69. Vector(D, B'_1) → v_1
  70. Vector(D, B'_3) → w_1
  71. Vector(D, B'_2) → i_1
  72. Circle(V, A) → g_2
  73. Midpoint(f') → W
  74. Circle(W, D) → h_2
  75. CircleArc(W, C, D) → p_2
  76. Point(q_2) → E
  77. Segment(A, E) → j_1
  78. Segment(E, D) → l_1
  79. OrthogonalLine(C, l_1) → m_1
  80. Intersect(l_1, m_1) → F
  81. Ray(C, E) → n_1
  82. Ray(D, A) → i_2
  83. Intersect(n_1, i_2) → H
  84. Ray(A, F) → l_2
  85. Intersect(f', l_2) → G
  86. Segment(H, G) → n
  87. Intersect(j_1, n) → M
  88. Intersect(l_1, n) → N
  89. Intersect(l_1, n) → A_1
  90. Distance(G, N) → distanceGN
  91. Distance(M, H) → distanceMH
  92. Angle(C, F, E) → α
  93. Angle(A, E, D) → β
  94. Segment(C, F) → m_2
  95. Distance(H, M) → distanceHM
  96. Intersect(n, m_2) → Z
  97. Distance(Z, G) → distanceZG
  98. Dilate(C, If[10 < e ≤ 11, 11 - e, 0], H) → B_1
  99. Segment(C, B_1) → a_1
  100. Segment(C, E) → b_1
  101. Segment(C, H) → n_2
  102. Dilate(A, If[10 < e ≤ 11, 11 - e, 0], H) → A'_3
  103. Segment(A, A'_3) → r_2
  104. Dilate(C, If[12 < e ≤ 13, 13 - e, 0], F) → D_1
  105. Segment(C, D_1) → f_1
  106. Dilate(A, If[11 < e ≤ 12, 12 - e, 0], E) → A'_4
  107. Dilate(D, If[11 < e ≤ 12, 12 - e, 0], E) → B'_4
  108. Segment(A, M) → g_1
  109. Segment(D, B'_4) → c_1
  110. Segment(A, A'_4) → e_1
  111. Intersect(f'', f''') → I_1
  112. Dilate(I_1, If[13 < e ≤ 14, 14 - e, 0], E) → J_1
  113. Vector(I_1, J_1) → d_1
  114. Translate(t, d_1) → t'_1
  115. Line(I_1, c_1) → h_1
  116. Point(h_1) → K_1
  117. Line(I_1, e_1) → p_1
  118. Point(p_1) → L_1
  119. Angle(L_1, I_1, A) → δ
  120. Rotate(t'_1, If[13 < e ≤ 14, ((-(e - 13)) * δ), (-δ)], J_1) → k_1
  121. Dilate(C, If[14 < e ≤ 15, 15 - e, 0], F) → O_1
  122. Ray(F, C) → q_1
  123. Point(q_1) → P_1
  124. Angle(D, C, P_1) → γ
  125. Vector(C, O_1) → r_1
  126. Translate(s'', r_1) → s'''_1
  127. Rotate(s'''_1, If[14 < e ≤ 15, ((e - 14) * γ), γ], O_1) → s_1
  128. Dilate(H, If[15 < e ≤ 16, 16 - e, 0], M) → H'
  129. Dilate(M, If[16 < e ≤ 17, 17 - e, 0], N) → M'
  130. Dilate(N, If[17 < e ≤ 18, 18 - e, 0], Z) → N'
  131. Dilate(Z, If[18 < e ≤ 19, 19 - e, 0], G) → Z'
  132. Segment(H, H') → t_1
  133. Segment(M, M') → f_2
  134. Segment(N, N') → s_2
  135. Segment(Z, Z') → t_2
  136. Rotate(H, If[19 < e ≤ 20, ((-(e - 19)) * π / 2), ((-π)) / 2], M) → H'_1
  137. Rotate(H', If[19 < e ≤ 20, ((-(e - 19)) * π / 2), ((-π)) / 2], M) → H''
  138. Segment(H'_1, H'') → a_2
  139. Dilate(M, If[20 < e ≤ 21, 21 - e, 0], Z) → M'_1
  140. Vector(M, M'_1) → u_2
  141. Translate(H'_1, u_2) → Q_1
  142. Translate(H'', u_2) → H'''
  143. Segment(Q_1, H''') → b_2
  144. Rotate(Q_1, If[21 < e ≤ 22, ((-(e - 21)) * π / 2), ((-π)) / 2], Z) → R_1
  145. Rotate(H''', If[21 < e ≤ 22, ((-(e - 21)) * π / 2), ((-π)) / 2], Z) → S_1
  146. Segment(R_1, S_1) → c_2
  147. Polygon(A, E, D) → poly2, b_3, a_3, e_2
  148. Polygon(D, F, C) → poly3, c_3, b_4, f_3
  149. Polygon(A, E, F, C, I_1) → poly4, a_4, e_3, f_4, c_4, i_3

AI Drawing Prompt Reference

Draw a dynamically transforming square, showing its path through scaling and rotation. The square starts at the center and changes size and position based on a vector. Illustrate the square's scaling and rotation paths, connecting the square's vertices to the center, and mark key intersection points and auxiliary arcs to create a dynamic geometric transformation.
The prompt above was compiled from the original drawing commands and is for reference only.