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Symmetry and Transformation of a Rectangle

Symmetry and Transformation of a Rectangle
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2014-08-08 10:42
VectorTransformationGeometric Construction
In collections Symmetry, Transformation and Tessellation
This example demonstrates the symmetry and transformation of a rectangle on a plane. Key mathematical concepts include geometric transformations, vectors, and reflections. Using GeoGebra commands such as Point, Vector, Mirror, and LineBisector, the construction of a rectangle and its symmetric figures is illustrated. Suitable for students at the junior high school level and above to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Midpoint(A, B) → E
  3. Midpoint(B, D) → F
  4. Midpoint(D, C) → G
  5. Midpoint(C, A) → H
  6. Midpoint(C, B) → I
  7. Vector(A, B) → u
  8. Vector(A, C) → v
  9. Vector(C, D) → w
  10. Vector(B, D) → a
  11. Segment(H, F) → b
  12. Segment(E, G) → c
  13. Segment(J, K) → e
  14. Segment(K, L) → f
  15. Segment(K, M) → g
  16. Segment(K, N) → h
  17. LineBisector(A, E) → j
  18. LineBisector(E, B) → k
  19. Mirror(cell1, j) → cell2
  20. Mirror(cell1, I) → cell3
  21. Mirror(cell2, I) → cell4
  22. Sequence(Translate[Sequence[Translate[tile, Vector[(n * u)]], n, -3, 3], Vector[(m * v)]], m, -3, 3) → tiling
  23. Line(H, F) → m

AI Drawing Prompt Reference

Draw a rectangle ABCD, then find its center points E, F, G, and H. Draw the diagonals AC and BD, and their midpoints I. Construct the sides of the rectangle using vectors u, v, w, and a. Draw line segments b, c, e, f, g, and h, and lines j and k. Mirror rectangle ABCD using line j and point I to get A'B'C'D'; then mirror A'B'C'D' using point I to get A''B''C''D''; finally, use vectors u and v to translate rectangle ABCD and create a grid of translated rectangles.
The prompt above was compiled from the original drawing commands and is for reference only.