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Identify Translation

Identify Translation
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2018-02-03 00:48
VectorCoordinate GeometryGeometric Construction
This example demonstrates the process of identifying translation transformations in a 2D coordinate system. Key math concepts include translation vectors, vector representation, line segments, and polygon construction. It uses commands like Polygon, Segment, Translate along with objects such as Textfield and InputBox for interactive learning, suitable for middle school and above studying 2D transformations, vectors, and geometric constructions.

GeoGebra Commands & Parameters

  1. Polygon((-1, 13.4), (30, 13.4), (30, 17), (-1, 17)) → TopBox, f, g, h, i
  2. Polygon((17.4, 15), (30, 15), (30, -1), (17.4, -1)) → RightBox, j, k, l, m
  3. Textfield(usertext1) → InputBox1
  4. Textfield(usertext2) → InputBox2
  5. Polygon((24, 13.5), (26, 13.5), (26, 12.5), (24, 12.5)) → Box1, n, p, q, r
  6. Polygon((24, 10), (26, 10), (26, 9), (24, 9)) → Box3, c, d, e, f_1
  7. Polygon((24, 8.9), (26, 8.9), (26, 7.9), (24, 7.9)) → Box4, g_1, h_1, i_1, j_1
  8. Polygon((24, 12.4), (26, 12.4), (26, 11.4), (24, 11.4)) → Box2, s, t, a, b
  9. Segment(A, B) → AB
  10. Segment(B, C) → BC
  11. Segment(C, A) → CA
  12. Translate(A, (htrans, vtrans)) → A'
  13. Translate(B, (htrans, vtrans)) → B'
  14. Translate(C, (htrans, vtrans)) → C'
  15. Segment(A', B') → AB'
  16. Segment(B', C') → BC'
  17. Segment(C', A') → CA'
  18. Segment(A, A + (htrans, 0)) → Ahoriz
  19. Segment(B, B + (htrans, 0)) → Bhoriz
  20. Segment(C, C + (htrans, 0)) → Choriz
  21. Segment(A + (htrans, 0), A + (htrans, vtrans)) → Avert
  22. Segment(B + (htrans, 0), B + (htrans, vtrans)) → Bvert
  23. Segment(C + (htrans, 0), C + (htrans, vtrans)) → Cvert

AI Drawing Prompt Reference

Draw a 2D coordinate system with four small rectangles and two large rectangles, colored differently. One group of rectangles is translated to the right and downward, showing the translation vector. Also, draw the edges of the original and translated rectangles, and the horizontal and vertical components of the translation vector to illustrate the composition of the translation transformation.
The prompt above was compiled from the original drawing commands and is for reference only.