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Rotation, Translation and Volume: Animation 36

Rotation, Translation and Volume: Animation 36
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2016-10-31 16:34
CircleVectorTransformationGeometric ConstructionSlider Animation
In collections Congruence Review 1
①This GeoGebra example dynamically demonstrates the construction of geometric figures under rotations and translations, integrating concepts of volume, arithmetic, addition, median lines, and fractions. ②Core mathematical concepts include rotation transformation, translation transformation, volume calculation, arithmetic operations, addition, median line properties, and fraction representation, all interconnected through dynamic geometric objects. ③Construction highlights: uses GeoGebra commands such as Circle, Point, Rotate, Angle, Vector, Segment, Intersect, CircleSector, Line, Dilate, and Translate, creating multiple points, segments, circles, sectors, vectors, and transformed objects, with a button controlling the animation. ④Suitable for middle or high school mathematics teaching or self-study, to intuitively understand the combination of geometric transformations and algebraic operations, and as a reference for teachers creating dynamic lessons.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Rotate(C, α, A) → C'
  4. Angle(C, A, C') → β
  5. Vector(A, C) → u
  6. Vector(A, C') → v
  7. Segment(A, B) → b
  8. Circle(D, b) → d
  9. Point(d) → E
  10. Rotate(E, α, D) → E'
  11. Angle(E, D, E') → γ
  12. Vector(D, E) → w
  13. Vector(D, E') → e
  14. Circle(A, (0.3 * b)) → f
  15. Circle(D, (0.3 * b)) → g
  16. Segment(A, C) → h
  17. Segment(A, C') → i
  18. Segment(D, E) → j
  19. Segment(D, E') → k
  20. Intersect(f, h, 1) → F
  21. Intersect(f, i, 1) → G
  22. Intersect(g, j, 1) → H
  23. Intersect(g, k, 1) → I
  24. CircleSector(A, F, G) → p
  25. Line(A, j) → l
  26. Intersect(f, l, 2) → J
  27. Angle(J, A, F) → δ
  28. Dilate(A, If[0 < m ≤ 1, 1 - m, 0], D) → A'
  29. Vector(A, A') → n
  30. Translate(p, n) → p'
  31. Rotate(p', If[1 < m ≤ 2, ((-(m - 1)) * δ), (-δ)], D) → p''