MathPlotAI Logo MathPlotAI

Transformations: Rotation, Reflection, Translation

Transformations: Rotation, Reflection, Translation
Loading the math board and drawing, please wait…
2017-09-12 13:54
Coordinate GeometryTransformationGeometric Construction
This example demonstrates three basic geometric transformations: rotation, reflection, and translation. It involves key mathematical concepts such as rotation, reflection, and translation. Using GeoGebra commands like Polygon, Dilate, Ray, Translate, Vector, and Rotate, the transformations can be constructed. Suitable for students at the junior high school level and above.

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 with vertices labeled. Construct a smaller or larger similar triangle by scaling it from one vertex. Rotate the original triangle around that same vertex by a given angle to form a second triangle. Translate the original triangle horizontally and vertically to create a third triangle, showing translation vectors as arrows. Reflect the original triangle across a line passing through a point on the x-axis and another fixed point to obtain a fourth triangle. Also mark the rotation angle and another related angle.
The prompt above was compiled from the original drawing commands and is for reference only.