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Combining Transformations Demo

Combining Transformations Demo
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2015-03-27 18:55
PolygonVectorCoordinate GeometryTransformationGeometric Construction
In collections Transformations (of shapes)
This GeoGebra worksheet demonstrates a series of sequential geometric transformations, including reflections, rotations, and translations. Core math concepts involve transformations, vectors, polygons, and coordinate geometry. It is constructed using commands like Line, Vector, If, Polygon, and objects such as N, M, g, J, ScaleFactor2, tr2ro, tr2re, tr2en, I, H, u, G, F, f, ScaleFactor1, A, O, tr1re, tr1en, tr1ro, Angle1, A', Angle2, L, K, v, tr1tr, button1, button2, button3, button4, B, C, D, E, poly1, a, b, c, d. Suitable for middle school and above students to explore the properties and combinations of geometric transformations.

GeoGebra Commands & Parameters

  1. Line(M, N) → g
  2. Vector(H, I) → u
  3. Line(F, G) → f
  4. If(tr1en ≟ 1, Dilate[A, ScaleFactor1, O], If[tr1re ≟ 1, Mirror[A, f], If[tr1ro ≟ 1, Rotate[A, Angle1, O], Translate[A, u]]]) → A'
  5. Vector(K, L) → v
  6. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  7. If(tr1en ≟ 1, Dilate[B, ScaleFactor1, O], If[tr1re ≟ 1, Mirror[B, f], If[tr1ro ≟ 1, Rotate[B, Angle1, O], Translate[B, u]]]) → B'
  8. If(tr1en ≟ 1, Dilate[C, ScaleFactor1, O], If[tr1re ≟ 1, Mirror[C, f], If[tr1ro ≟ 1, Rotate[C, Angle1, O], Translate[C, u]]]) → C'
  9. If(tr1en ≟ 1, Dilate[D, ScaleFactor1, O], If[tr1re ≟ 1, Mirror[D, f], If[tr1ro ≟ 1, Rotate[D, Angle1, O], Translate[D, u]]]) → D'
  10. If(tr1en ≟ 1, Dilate[E, ScaleFactor1, O], If[tr1re ≟ 1, Mirror[E, f], If[tr1ro ≟ 1, Rotate[E, Angle1, O], Translate[E, u]]]) → E'
  11. Polygon(A', B', C', D', E') → poly1', a', b', c', d', e'
  12. If(tr2en ≟ 1, Dilate[B', ScaleFactor2, J], If[tr2re ≟ 1, Mirror[B', g], If[tr2ro ≟ 1, Rotate[B', Angle2, J], Translate[B', v]]]) → B''
  13. If(tr2en ≟ 1, Dilate[C', ScaleFactor2, J], If[tr2re ≟ 1, Mirror[C', g], If[tr2ro ≟ 1, Rotate[C', Angle2, J], Translate[C', v]]]) → C''
  14. If(tr2en ≟ 1, Dilate[D', ScaleFactor2, J], If[tr2re ≟ 1, Mirror[D', g], If[tr2ro ≟ 1, Rotate[D', Angle2, J], Translate[D', v]]]) → D''
  15. If(tr2en ≟ 1, Dilate[E', ScaleFactor2, J], If[tr2re ≟ 1, Mirror[E', g], If[tr2ro ≟ 1, Rotate[E', Angle2, J], Translate[E', v]]]) → E''
  16. If(tr2en ≟ 1, Dilate[A', ScaleFactor2, J], If[tr2re ≟ 1, Mirror[A', g], If[tr2ro ≟ 1, Rotate[A', Angle2, J], Translate[A', v]]]) → A''
  17. Polygon(A'', B'', C'', D'', E'') → poly1'', a'', b'', c'', d'', e''
  18. Polygon(P, Q, R, S, T) → poly2, p, q, r, s, t

AI Drawing Prompt Reference

Draw a pentagon and apply a series of geometric transformations, including reflection, rotation, and translation, to demonstrate the process and results. Each transformation generates a new pentagon, labeled with the type and parameters of the transformation. Finally, combine all transformed pentagons to form a nested sequence, clearly showing the叠加 effect of transformations.
The prompt above was compiled from the original drawing commands and is for reference only.