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Drawing Transformed Images

Drawing Transformed Images
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2020-06-24 03:33
PolygonVectorCoordinate Geometry
This example demonstrates how to draw the image of a shape under a translation transformation using GeoGebra. Key math concepts include vectors, polygons, coordinate geometry, and transformation. It utilizes commands like Random, Vector, Polygon, Segment, Translate, DynamicCoordinates, and If. Suitable for high school students learning geometric transformations and their applications.

GeoGebra Commands & Parameters

  1. Random(-6, 6) → e_1
  2. Random(-6, 6) → w
  3. Vector((0, 0), (w, e_1)) → u_1
  4. Random(-3, 3) → a
  5. Random(-3, 3) → b
  6. Random(-3, 3) → c
  7. Random(-3, 3) → d
  8. Random(-3, 3) → e
  9. Random(-3, 3) → f
  10. Random(-3, 3) → g
  11. Random(-3, 3) → h
  12. Polygon(A, B, C, D) → q1, a_1, b_1, c_1, d_1
  13. Segment(A, B) → i
  14. Segment(B, C) → j
  15. Segment(C, D) → k
  16. Segment(D, A) → l
  17. Random(-2, 2) → m
  18. Random(-2, 2) → n
  19. Random(-1, 1) → o
  20. Translate(B, u_1) → B'
  21. Translate(C, u_1) → C'
  22. Translate(D, u_1) → D'
  23. Translate(A, u_1) → A'
  24. Polygon(A', B', C', D') → q1', a', b', c', d'
  25. DynamicCoordinates(G, round(x(G)), round(y(G))) → A_1
  26. DynamicCoordinates(H, round(x(H)), round(y(H))) → B_1
  27. DynamicCoordinates(E, round(x(E)), round(y(E))) → C_1
  28. DynamicCoordinates(F, round(x(F)), round(y(F))) → D_1
  29. Polygon(A_1, B_1, C_1, D_1) → q2, p, r, s, t
  30. Segment(C_1, D_1) → f_1
  31. Segment(A_1, D_1) → g_1
  32. Segment(A_1, B_1) → h_1
  33. Segment(B_1, C_1) → i_1
  34. Segment(D_1, A_1) → j_1
  35. If(A_1 ≟ A' ∧ B_1 ≟ B' ∧ C_1 ≟ C' ∧ D_1 ≟ D', "Correct!", "No. Try again.") → text1

AI Drawing Prompt Reference

Draw a random quadrilateral with vertices chosen randomly in the range -3 to 3. Create a random translation vector starting at the origin with endpoint coordinates between -6 and 6. Translate the original quadrilateral by this vector to form a congruent second quadrilateral. Additionally, place four draggable points on the canvas that snap to nearest integer coordinates, and connect them to form a third quadrilateral. Finally, display text that says "Correct!" when the third quadrilateral's vertices exactly match the translated quadrilateral's vertices, otherwise show "No. Try again.".
The prompt above was compiled from the original drawing commands and is for reference only.