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Vector Addition and Subtraction Exercises

Vector Addition and Subtraction Exercises
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2014-01-07 12:30
VectorCoordinate GeometryGeometric Construction
In collections Complex Numbers as Vectors
This example demonstrates interactive exercises on vector addition and subtraction, highlighting geometric transformations and coordinate geometry. It constructs vectors, polygons, and intersections using commands like Polygon, Segment, Intersect, Vector, and Translate in GeoGebra, suitable for high school mathematics instruction or student exploration of vector properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, a, b, c, d, e, C_2, D_1, E_1
  2. Segment(E_1, A) → f
  3. Segment(A, B) → g
  4. Segment(B, C_2) → h
  5. Segment(C_2, D_1) → i
  6. Segment(D_1, E_1) → j
  7. Segment(E_1, C_2) → k
  8. Segment(D_1, B) → l
  9. Segment(D_1, A) → m
  10. Segment(C_2, A) → n
  11. Segment(E_1, B) → p
  12. Intersect(n, p) → F
  13. Intersect(l, n) → G
  14. Intersect(k, l) → H
  15. Intersect(k, m) → I
  16. Intersect(m, p) → J
  17. Vector(E_1, D_1) → u
  18. Vector(E_1, H) → v
  19. Vector(H, D_1) → w
  20. Translate(K, u) → K'
  21. Vector(K, K') → z
  22. Translate(L, w) → L'
  23. Vector(L, L') → q
  24. Translate(M, v) → M'
  25. Vector(M, M') → r
  26. Vector(C_2, B) → s
  27. Vector(C_2, D_1) → t
  28. Translate(O, s) → O'
  29. Vector(O, O') → u_1
  30. Translate(N, t) → N'
  31. Vector(N, N') → v_1
  32. Vector(D_1, B) → w_1
  33. Translate(P, w_1) → P'
  34. Vector(P, P') → z_1
  35. Vector(A, E_1) → a_1
  36. Translate(Q, a_1) → Q'
  37. Vector(Q, Q') → b_1
  38. Vector(H, C_2) → c_1
  39. Translate(R, c_1) → R'
  40. Vector(R, R') → d_1
  41. Vector(D_1, A) → e_1
  42. Translate(S, e_1) → S'
  43. Vector(S, S') → f_1
  44. Vector(D_1, I) → g_1
  45. Translate(T, g_1) → T'
  46. Vector(T, T') → h_1
  47. Vector(I, J) → i_1
  48. Vector(J, F) → j_1
  49. Vector(F, G) → k_1
  50. Vector(G, H) → l_1
  51. Vector(H, I) → m_1
  52. Translate(U, i_1) → U'
  53. Vector(U, U') → n_1
  54. Translate(V, j_1) → V'
  55. Vector(V, V') → p_1
  56. Translate(W, k_1) → W'
  57. Vector(W, W') → q_1
  58. Translate(Z, l_1) → Z'
  59. Vector(Z, Z') → r_1
  60. Translate(A_1, m_1) → B_1
  61. Vector(A_1, B_1) → s_1
  62. Segment(A_2, B_2) → g_2
  63. Intersect(i, j) → D
  64. Intersect(h, i) → C
  65. Intersect(f, j) → E
  66. Vector(D, A) → t_1
  67. Vector(A, D) → u_2
  68. Translate(G_1, t_1) → H_1

AI Drawing Prompt Reference

Draw a pentagon and connect each vertex to the intersection points of the diagonals, forming several triangles. Then, draw vectors from the center of the pentagon representing vector addition and subtraction. Finally, translate and draw the opposite vectors to illustrate geometric transformations of the vectors.
The prompt above was compiled from the original drawing commands and is for reference only.