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Translation Exploration by Jed Butler

Translation Exploration by Jed Butler
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2015-01-31 13:49
VectorTransformationGeometric Construction
In collections Transformations Stations
This example investigates what changes and what remains unchanged in a translation transformation. Key mathematical concepts include translation, basic properties of geometric figures. It uses Polygon, Intersect, Vector, Translate, Segment commands in GeoGebra. Suitable for middle school and above students for geometric construction and transformation exploration.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Intersect(xAxis, yAxis) → D
  3. Vector(D, E) → u
  4. Translate(A, u) → A'
  5. Translate(B, u) → B'
  6. Translate(C, u) → C'
  7. Polygon(A', B', C') → poly1', c', a', b'
  8. Segment((0, 0), (x(E), 0)) → d
  9. Segment((0, 0), (0, y(E))) → e
  10. Segment(B', B) → f
  11. Segment(A', A) → g
  12. Segment(C', C) → h

AI Drawing Prompt Reference

Draw a triangle ABC, then find the intersection point D of the x-axis and y-axis. Draw a vector u from D to point E. Translate triangle ABC along vector u to get triangle A'B'C'. Finally, draw the projections of point E onto the x-axis and y-axis as line segments d and e, and the sides A'B', A'C', and B'C' of triangle A'B'C'.
The prompt above was compiled from the original drawing commands and is for reference only.