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Exploring Translations on a Coordinate Grid

Exploring Translations on a Coordinate Grid
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2019-03-13 02:22
PolygonVectorCoordinate GeometryGeometric Construction
This example demonstrates geometric transformations, specifically translations, on a coordinate grid. It involves core math concepts like Translation, Integers, Vectors, Linear Regression, Random Variables, and Piecewise Functions. Constructed using GeoGebra commands such as Polygon, Vector, Translate, and objects like Vector_3y, Vector_3x, A, B, etc. Aimed at 8-10th grade introductory geometry students.

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