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Exploring Translations by Mr. Watson (6)

Exploring Translations by Mr. Watson (6)
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2016-02-16 01:51
PolygonVectorCoordinate GeometryGeometric Construction
In collections Geometry Transformations
This example demonstrates geometric transformations on a coordinate grid, focusing on translation. Core math concepts include vectors, polygons, and coordinate geometry. It is constructed using GeoGebra commands like Polygon, Vector, and Translate, and objects such as A, B, C, D, and vectors. Aimed at 8-10th grade students for an introduction to geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Vector(E, F) → u
  3. Translate(A_1, u) → G
  4. Translate(B_1, u) → H
  5. Translate(C_1, u) → I
  6. Translate(D_1, u) → J
  7. Vector(E, K) → v
  8. Translate(A_1, v) → L
  9. Translate(B_1, v) → M
  10. Translate(C_1, v) → N
  11. Translate(D_1, v) → O
  12. Vector(E, P) → w
  13. Translate(A_1, w) → Q
  14. Translate(B_1, w) → R
  15. Translate(C_1, w) → S
  16. Translate(D_1, w) → T
  17. Translate(A, u) → A'_1
  18. Translate(B, u) → B'_1
  19. Translate(C, u) → C'_1
  20. Translate(D, u) → D'_1
  21. Polygon(A'_1, B'_1, C'_1, D'_1) → poly1', a', b', c', d'
  22. Translate(A_1, u) → U
  23. Translate(B_1, u) → V
  24. Translate(C_1, u) → W
  25. Translate(D_1, u) → Z
  26. Polygon(U, V, W, Z) → poly2, u_1, v_1, w_1, z
  27. Translate(A, v) → A'_2
  28. Translate(B, v) → B'_2
  29. Translate(C, v) → C'_2
  30. Translate(D, v) → D'_2
  31. Polygon(A'_2, B'_2, C'_2, D'_2) → poly1'_1, a'_1, b'_1, c'_1, d'_1
  32. Translate(A_1, v) → E_1
  33. Translate(B_1, v) → F_1
  34. Translate(C_1, v) → G_1
  35. Translate(D_1, v) → H_1
  36. Polygon(E_1, F_1, G_1, H_1) → poly3, e_1, f_1, g_1, h_1
  37. Translate(A, w) → A'_3
  38. Translate(B, w) → B'_3
  39. Translate(C, w) → C'_3
  40. Translate(D, w) → D'_3
  41. Polygon(A'_3, B'_3, C'_3, D'_3) → poly1'_2, a'_2, b'_2, c'_2, d'_2
  42. Translate(A_1, w) → I_1
  43. Translate(B_1, w) → J_1
  44. Translate(C_1, w) → K_1
  45. Translate(D_1, w) → L_1
  46. Polygon(I_1, J_1, K_1, L_1) → poly4, i_1, j_1, k_1, l_1
  47. Translate(A'_3, Vector[(0, 0)]) → A''
  48. Polygon(A_4, B_4, C_4, D_4) → poly1_2, a_2, b_2, c_2, d_2
  49. Polygon(A_3, B_3, C_3, D_3) → poly1_3, a_3, b_3, c_3, d_3
  50. Polygon(A_5, B_5, C_5, D_5) → poly1_4, a_4, b_4, c_4, d_4
  51. Polygon(A_6, B_6, C_6, D_6) → poly1_5, a_5, b_5, c_5, d_5

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, then translate it along vector u to get quadrilateral A'B'C'D', and along vector v to get quadrilateral A''B''C''D''. Next, translate quadrilateral A'''B'''C'''D''' back to the origin to get the final quadrilateral A''B''C''D''.
The prompt above was compiled from the original drawing commands and is for reference only.