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Transformations: Mapping Rectangles onto Rectangles

Transformations: Mapping Rectangles onto Rectangles
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2016-08-04 00:00
VectorTransformationGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 1) Congruence (Vol 1) Over 80 Resources CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 GCSE Higher Ch8 Transformations & Constructions CCSS High School: Geometry (Congruence) Volume 1 Transformations! (Geometry) Transformations/Symmetry
This example demonstrates how to map one rectangle onto another using geometric transformations. Key mathematical concepts include geometric transformations, linear equations, and vectors. Using GeoGebra commands such as Random, Line, Rotate, and Translate, the transformation process can be constructed. Suitable for students at the junior high school level and above to learn about geometric transformations and related concepts.

GeoGebra Commands & Parameters

  1. Random(1, 359) → p
  2. Line(A, B) → f
  3. OrthogonalLine(A, f) → g
  4. Point(g) → C
  5. Ray(A, C) → i
  6. Point(i) → D
  7. OrthogonalLine(D, i) → j
  8. OrthogonalLine(B, f) → h
  9. Intersect(h, j) → E
  10. Segment(E, D) → m
  11. Midpoint(m) → H
  12. Segment(A, B) → k
  13. Midpoint(k) → I
  14. Midpoint(H, I) → J
  15. Random(-3, 3) → c
  16. Random(-4, 4) → o
  17. Polygon(A, B, E, D) → poly1, a, b, e, d
  18. Segment(B, E) → l
  19. Segment(D, A) → n
  20. Angle(poly1) → α, β, γ, δ
  21. Rotate(A, (p * π / 180), J) → A'
  22. Rotate(B, (p * π / 180), J) → B'
  23. Rotate(E, (p * π / 180), J) → E'
  24. Rotate(D, (p * π / 180), J) → D'
  25. Polygon(A', B', E', D') → poly1', a', b', e', d'
  26. Vector(J, (x(J) + (sqrt(c^(2) + o^(2)) * cos((p * π / 180))), y(J) + (sqrt(c^(2) + o^(2)) * sin((p * π / 180))))) → u
  27. Translate(A', u) → A''
  28. Translate(B', u) → B''
  29. Translate(E', u) → E''
  30. Translate(D', u) → D''
  31. Polygon(A'', B'', E'', D'') → poly1'', a'', b'', e'', d''
  32. Segment(D'', E'') → q
  33. Segment(E'', B'') → r
  34. Segment(B'', A'') → s
  35. Segment(A'', D'') → t