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Rotation and Translation by Patrick Clément

Rotation and Translation by Patrick Clément
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2016-04-15 05:25
PolygonVectorTransformation
This example demonstrates how to generate a parallelogram using rotation and translation. Key mathematical concepts include rotation, translation, and polygons. It utilizes commands such as Rotate, Polygon, Sequence, and Vector in GeoGebra. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Rotate(B, (-(90°)), A) → B'
  2. Rotate(C, (-(90°)), A) → C'
  3. Rotate(D, (-(90°)), A) → D'
  4. Rotate(E, (-(90°)), A) → E'
  5. Polygon({A, B, C, D, E, E', D', C', B'}) → poly1
  6. Sequence(Polygon[Rotate[A, i, A], Rotate[B, i, A], Rotate[C, i, A], Rotate[D, i, A], Rotate[E, i, A], Rotate[E', i, A], Rotate[D', i, A], Rotate[C', i, A], Rotate[B', i, A]], i, 90°, 360°, 90°) → liste1
  7. Sequence(Rotate[poly1, i, E], i, 90°, 360°, 90°) → liste2
  8. Vector(E', E) → u
  9. Sequence(Translate[liste1, Vector[(i * u)]], i, 1, 5) → liste3
  10. Rotate(E', 90°, E) → E''
  11. Vector(E'', E) → v
  12. Sequence(Translate[liste3, Vector[(i * v)]], i, 1, 3) → liste4