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Translation Transformations

Translation Transformations
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2022-06-17 21:57
VectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates transformations on the Cartesian plane, specifically translations, by moving shapes to show the effect of the transformation. Core math concepts include vectors, geometric transformations, and coordinate geometry. It utilizes commands and objects like Polygon, Vector, and Translate from GeoGebra as outlined in the construction summary. Suitable for high school students learning coordinate geometry and geometric transformations to understand the principles and applications of translation.

GeoGebra Commands & Parameters

  1. Polygon(C, D, B) → poly1, b, c, d
  2. Dilate(C, a, A) → C'_1
  3. Dilate(D, a, A) → D'_1
  4. Dilate(B, a, A) → B'_1
  5. Polygon(C'_1, D'_1, B'_1) → poly1'_1, b', c', d'
  6. Ray(A, C) → e
  7. Ray(A, B) → f
  8. Ray(A, D) → g
  9. Translate(C, Vector[(horz, vert)]) → C'_2
  10. Translate(D, Vector[(horz, vert)]) → D'_2
  11. Translate(B, Vector[(horz, vert)]) → B'_2
  12. Polygon(C'_2, D'_2, B'_2) → poly1'_2, b'_1, c'_1, d'_1
  13. Vector(C, C'_2) → u
  14. Vector(B, B'_2) → v
  15. Vector(D, D'_2) → w
  16. Rotate(C, (-α), A) → C'_3
  17. Rotate(D, (-α), A) → D'_3
  18. Rotate(B, (-α), A) → B'_3
  19. Polygon(C'_3, D'_3, B'_3) → poly1'_3, b'_2, c'_2, d'_2
  20. Line(F, E) → h
  21. Mirror(C, h) → C'
  22. Mirror(D, h) → D'
  23. Mirror(B, h) → B'
  24. Polygon(C', D', B') → poly1', b'_3, c'_3, d'_3
  25. Vector(A, G) → z
  26. Angle(G, A, H) → β
  27. Polygon(I, J, K, L) → poly2, i, j, k_1, l
  28. Polygon(M, N, O, P) → poly3, m, n, o, p
  29. Corner(text22, 1) → c1
  30. Corner(text22, 2) → c2

AI Drawing Prompt Reference

On a coordinate plane, draw an initial triangle formed by three points. Choose a center point and first construct a scaled copy of the triangle to show one transformed position. Then, using the same translation direction and magnitude, translate each vertex of that scaled triangle to produce a second transformed triangle. From the same center, add a rotation by a specified angle in the opposite direction to obtain a third triangle position. Also include the needed rays from the center to define the rotation, draw a reference line used for reflection, and finally depict the triangle mirrored across that line to show the mirror image.
The prompt above was compiled from the original drawing commands and is for reference only.