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Transformations Demonstration

Transformations Demonstration
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2013-05-01 04:33
VectorTransformationGeometric Construction
In collections Reflections rotations Translations
This example demonstrates four key transformations: translation, rotation, reflection, and dilation. Using GeoGebra commands such as Point, Polygon, Translate, Rotate, and Dilate, the process of these transformations is clearly illustrated. Suitable for students at the junior high school level and above to learn about geometric transformations.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 2]) → B
  2. Polygon(A, B, C) → poly1, c, a, b
  3. Vector(E, F) → u
  4. Translate(A, u) → A'
  5. Translate(B, u) → B'
  6. Translate(C, u) → C'
  7. Polygon(A', B', C') → poly1', c', a', b'
  8. Rotate(A, -(f°), D) → A'_1
  9. Rotate(B, -(f°), D) → B'_1
  10. Rotate(C, -(f°), D) → C'_1
  11. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  12. Dilate(A, g, D) → A'_2
  13. Dilate(B, g, D) → B'_2
  14. Dilate(C, g, D) → C'_2
  15. Polygon(A'_2, B'_2, C'_2) → poly1'_2, c'_2, a'_2, b'_2
  16. Intersect(b'_2, c'_2) → G
  17. Intersect(b, c) → H
  18. Intersect(b'_2, a'_2) → I
  19. Intersect(b, a) → J
  20. If(f ≟ 0, "", "Rotation " + (If[f < 0, -f, f]) + "∘ " + (If[f ≟ 180 ∨ f ≟ 360 ∨ f ≟ -180 ∨ f ≟ -360, "", If[f < 0, "anti-clockwise", "clockwise"]]) + " around (" + (x(D)) + "," + (y(D)) + ")") → text2
  21. Line(K, L) → j
  22. Mirror(A, j) → A'_3
  23. Mirror(B, j) → B'_3
  24. Mirror(C, j) → C'_3
  25. Polygon(A'_3, B'_3, C'_3) → poly1'_3, c'_3, a'_3, b'_3
  26. Slope(j) → m
  27. If(g ≟ 1 ∨ g ≟ 0, "", "Enlarge, scale factor " + g + " from centre (" + (x(D)) + "," + (y(D)) + ")") → text3
  28. Line(D, C'_2) → i
  29. Line(D, B'_2) → l
  30. Line(A'_2, D) → h

AI Drawing Prompt Reference

Draw a circle with center A and radius 2, then construct a triangle with points B and C on the circle. Define a vector u and translate the triangle along u to get a new triangle. Then rotate the new triangle 90 degrees counterclockwise around point D, translate it again, and finally enlarge it with a scale factor of 2 from point D. Draw the enlarged triangle and find the intersection points of the corresponding sides of the enlarged and original triangles.
The prompt above was compiled from the original drawing commands and is for reference only.