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Animation 75: Geometric Transformations and Function Demonstration

Animation 75: Geometric Transformations and Function Demonstration
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2016-06-27 09:06
VectorFunctionCoordinate GeometryTransformationGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates transformations and combinations of shapes like parallelograms, isosceles triangles, and circular sectors through animation; involves core concepts such as congruence, similarity, ratios, quadratic functions, and coordinate geometry; constructed using commands like Line, Slope, PointIn, Vector, Translate, Segment, Circle, Intersect, CircleSector, Dilate, CircleArc, Rotate, Polygon; suitable for high school mathematics teaching to understand geometric transformations and function graphs relations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Slope(a) → m
  3. PointIn(c) → C
  4. Line(C, a) → e
  5. Vector(A, B) → u
  6. Translate(C, u) → C'
  7. Segment(B, C') → f
  8. Segment(C, C') → g
  9. Segment(A, B) → h
  10. Segment(A, C) → d
  11. Circle(A, (0.2 * Min[d, h])) → p
  12. Intersect(p, d, 1) → F
  13. Intersect(p, h, 1) → G
  14. Circle(B, (0.2 * Min[d, h])) → q
  15. Intersect(q, h, 1) → H
  16. Intersect(q, f, 1) → I
  17. CircleSector(A, G, F) → r
  18. CircleSector(B, I, H) → s
  19. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], C') → A'_2
  20. Vector(A, A'_2) → v
  21. Translate(r, v) → r'
  22. CircleArc(A, G, F) → t
  23. Rotate(r', If[1 < k ≤ 2, ((k - 1) * π), 3.141592653589793], C') → r''
  24. Dilate(B, If[2 < k ≤ 3, 3 - k, 0], C) → B'_1
  25. Vector(B, B'_1) → w
  26. Translate(s, w) → s'
  27. Rotate(s', If[3 < k ≤ 4, ((k - 3) * π), 3.141592653589793], C) → s''
  28. CircleArc(B, I, H) → d_1
  29. Polygon(A, B, C', C) → poly1, a_1, b_1, c', c_1