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Similarity Transformation of Shapes

Similarity Transformation of Shapes
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2016-05-11 09:28
VectorCoordinate GeometryTransformation
This example demonstrates the similarity transformation of shapes, involving key mathematical concepts such as vectors and coordinate geometry. Using GeoGebra commands like Dilate (similarity transformation), Line (line), Polygon (polygon), etc., the construction of transformed shapes is illustrated. Suitable for students at the junior high school level and above to learn about the concept and application of similarity transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → S
  2. Dilate(A, a, S) → A'
  3. Dilate(B, a, S) → B'
  4. Dilate(A, n, C) → A''
  5. Dilate(B, n, C) → B''
  6. Line(A', A) → d
  7. Line(B', B) → e
  8. Line(A'', A) → f_1
  9. Line(B'', B) → g_1
  10. Polygon(A, B, 4) → poly1, f, g, h, i, D, E
  11. Midpoint(h) → F
  12. Circle(F, f) → c
  13. OrthogonalLine(F, f) → j
  14. Line(E, D) → r
  15. Intersect(c, r, 1) → J
  16. Intersect(c, j, 2) → K
  17. Intersect(c, r, 2) → L
  18. Dilate(A, n, C) → A'_1
  19. Dilate(E, n, C) → E'
  20. Dilate(J, n, C) → J'
  21. Dilate(K, n, C) → K'
  22. Dilate(L, n, C) → L'
  23. Dilate(D, n, C) → D'
  24. Dilate(B, n, C) → B'_1
  25. Dilate(A, a, S) → A'_2
  26. Dilate(E, a, S) → E'_1
  27. Dilate(J, a, S) → J'_1
  28. Dilate(K, a, S) → K'_1
  29. Dilate(L, a, S) → L'_1
  30. Dilate(D, a, S) → D'_1
  31. Dilate(B, a, S) → B'_2
  32. Polygon(A, B, 5) → poly2, k, l, m, p, q, G, H, I
  33. Polygon(A'', B'', 5) → poly3, s, t, b, h_1, i_1, M, N, O
  34. Polygon(A', B', 5) → poly4, j_1, k_1, l_1, m_1, n_1, P, Q, R