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Geometric Dilation and Function Transformation

Geometric Dilation and Function Transformation
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2012-02-19 20:10
FunctionCoordinate GeometryTransformation
In collections Transformation-Rotation Transformation-Reflection Dilations Boy in Dilation
This example demonstrates how scaling operations affect the size and position of shapes and how function graphs change under scaling. Key mathematical concepts include geometric transformations, function graphs, and coordinate geometry. Construction involves GeoGebra commands such as Intersect, Rotate, Angle, Line, etc. It is suitable for middle or high school mathematics to understand scaling transformations and their impact on function graphs.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Rotate(B, 45*°, A) → B'
  4. Angle(B, A, B') → α
  5. Line(A, B') → d
  6. Mirror(E, yAxis) → E'
  7. Point(yAxis) → C
  8. Circle(A, C) → c
  9. Rotate(C, 30*°, A) → m
  10. Angle(C, A, m) → β
  11. Rotate(m, 30*°, A) → p
  12. Angle(m, A, p) → γ
  13. Rotate(A, 330*°, C) → A'
  14. Angle(A', C, A) → δ
  15. Rotate(C, 30*°, A) → C'_1
  16. Angle(C, A, C'_1) → ε
  17. Rotate(C, 330*°, A) → q
  18. Angle(q, A, C) → ζ
  19. Rotate(q, 330*°, A) → t
  20. Angle(t, A, q) → η
  21. Rotate(C, 35*°, A) → C'_3
  22. Angle(C, A, C'_3) → θ
  23. Rotate(C, 38*°, A) → n
  24. Angle(C, A, n) → ι
  25. Mirror(n, f) → o
  26. Mirror(o, yAxis) → s
  27. Mirror(n, yAxis) → r
  28. Mirror(A, yAxis) → A'_1
  29. Circle(E', 0.25) → e
  30. Circle(E, 0.25) → g
  31. Center(c) → K
  32. Point(yAxis) → L
  33. Circle(L, 0.3) → q_1
  34. Intersect(c, xAxis, 1) → F_2
  35. Circle(A_2, R_1) → c_1
  36. Circle(S_1, 0.25 * rr) → h_1
  37. Circle(Z_1, 0.25 * rr) → k_1
  38. Circle(A, 0.7) → h
  39. Center(h) → F
  40. Midpoint(G, A) → H
  41. Mirror(H, A) → H'
  42. Distance(A_2, B_2) → 거리A2B2
  43. Circumference(h) → 둘레h
  44. Circle(A_2, 0.7 * rr) → k
  45. Circle(B_2, 0.25 * rr) → p_1
  46. Circle(C_2, 0.25 * rr) → r_1
  47. Circle(E_2, 0.3 * rr) → s_1
  48. Textfield(rr) → 텍스트필드1
  49. Semicircle(p, m) → t_1
  50. Semicircle(o, n) → c_2
  51. Semicircle(q, t) → d_2
  52. Semicircle(r, s) → e_2
  53. Circle(H, 0.25) → f_2
  54. Circle(H', 0.25) → g_2
  55. Textfield(b) → 텍스트필드3
  56. Semicircle(O_1, R_1) → d_1
  57. Semicircle(P_1, Q_1) → e_1
  58. Semicircle(T_1, W_1) → f_1
  59. Semicircle(U_1, V_1) → g_1
  60. Intersect(c, yAxis, 1) → G_2
  61. Intersect(c, xAxis, 1) → H_2
  62. Intersect(c, xAxis, 2) → I_2
  63. Intersect(c, yAxis, 2) → J_2
  64. Segment(center, H_2) → i
  65. Segment(center, G_2) → j
  66. Segment(center, T_2) → b_1
  67. Segment(center, S_2) → l_1
  68. Textfield(a) → 텍스트필드2
  69. Segment(center, U_2) → l

AI Drawing Prompt Reference

Draw a geometric illustration showing dilation and function transformation. Start by plotting the coordinate axes and marking their intersection point. Create a point and rotate it around the intersection to form a line. Then, draw a circle and repeatedly rotate it around the intersection to create multiple circles. Finally, add several circles and points, adjusting their positions and sizes to demonstrate how scaling operations affect the size and position of shapes and how function graphs change under scaling.
The prompt above was compiled from the original drawing commands and is for reference only.