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Reflection Transformation Demo by mathspace

Reflection Transformation Demo by mathspace
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2014-02-07 10:33
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the reflection transformation of points, lines, and polygons, highlighting symmetry and geometric properties. It involves core math concepts like geometric transformations and coordinate geometry. Construction uses commands such as Polygon, Line, Mirror, Vector, and Rotate to create and reflect shapes. Suitable for high school mathematics instruction on understanding reflections in the coordinate plane.

GeoGebra Commands & Parameters

  1. Polygon(C, D, B) → poly1, b, c, d
  2. Dilate(C, a, A) → C'_1
  3. Dilate(D, a, A) → D'_1
  4. Dilate(B, a, A) → B'_1
  5. Polygon(C'_1, D'_1, B'_1) → poly1'_1, b', c', d'
  6. Ray(A, C) → e
  7. Ray(A, B) → f
  8. Ray(A, D) → g
  9. Translate(C, Vector[(horz, vert)]) → C'_2
  10. Translate(D, Vector[(horz, vert)]) → D'_2
  11. Translate(B, Vector[(horz, vert)]) → B'_2
  12. Polygon(C'_2, D'_2, B'_2) → poly1'_2, b'_1, c'_1, d'_1
  13. Vector(C, C'_2) → u
  14. Vector(B, B'_2) → v
  15. Vector(D, D'_2) → w
  16. Rotate(C, (-α), A) → C'_3
  17. Rotate(D, (-α), A) → D'_3
  18. Rotate(B, (-α), A) → B'_3
  19. Polygon(C'_3, D'_3, B'_3) → poly1'_3, b'_2, c'_2, d'_2
  20. Point(xAxis) → E
  21. Line(F, E) → h
  22. Mirror(C, h) → C'
  23. Mirror(D, h) → D'
  24. Mirror(B, h) → B'
  25. Polygon(C', D', B') → poly1', b'_3, c'_3, d'_3
  26. Vector(A, G) → z
  27. Angle(G, A, H) → β

AI Drawing Prompt Reference

Draw a triangle ABC, then translate it horizontally and vertically around point A to get triangle A'B'C'. Next, rotate triangle A'B'C' counterclockwise around point A to get triangle A''B''C''. Finally, draw a line h parallel to the x-axis and mirror triangle A''B''C'' across line h to get triangle A'''B'''C'''.
The prompt above was compiled from the original drawing commands and is for reference only.