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Dilation Shape 1: Interactive Polygon Scaling

Dilation Shape 1: Interactive Polygon Scaling
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2016-05-11 09:24
PolygonTransformationGeometric ConstructionSlider Animation
This GeoGebra example demonstrates the dilation (scaling) transformation of polygons about a center point, showing how shapes enlarge or shrink proportionally. The core mathematical concept is dilation, involving similarity, scale factor, and the property that corresponding points lie on lines through the center with distances scaled by the factor. Construction highlights: using Polygon to create original polygons, Intersect to find intersection points, and Dilate to generate multiple scaled copies (poly1 through poly6), with associated points (A, B, C_1, D, etc.) and curves (f, g, h_2, etc.) enriching the visual. Suitable for middle and high school geometry lessons on similarity transformations, exploring how scale factor affects side lengths, area, and perimeter, and for dynamic investigations of transformation properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h_2, i, C_1, D
  2. Polygon(D, C_1, 4) → poly2, j, k, l, m, E, F
  3. Polygon(F, E, 4) → poly3, n_2, p, q, r, G, H
  4. Polygon(H, G, 4) → poly4, s, t, a_2, b, I, J
  5. Polygon(J, I, 4) → poly5, c, d, e, f_1, K, L
  6. Polygon(K, I, 4) → poly6, g_1, h_1, i_1, j_1, M, N
  7. Polygon(N, M, 4) → poly7, k_1, l_1, m_1, n_1, O, P
  8. Polygon(G, E, 4) → poly8, p_1, q_1, r_1, s_1, Q, R
  9. Polygon(A, L, P, O, I, G, R, Q, E, B) → poly9, a_1, b_1, l_2, p_2, o, i_2, g_2, r_2, q_2, e_1
  10. Intersect(xAxis, yAxis) → S
  11. Dilate(A, a, S) → A'
  12. Dilate(L, a, S) → L'
  13. Dilate(P, a, S) → P'
  14. Dilate(O, a, S) → O'
  15. Dilate(I, a, S) → I'
  16. Dilate(G, a, S) → G'
  17. Dilate(R, a, S) → R'
  18. Dilate(Q, a, S) → Q'
  19. Dilate(E, a, S) → E'
  20. Dilate(B, a, S) → B'
  21. Polygon(A', L', P', O', I', G', R', Q', E', B') → poly9', a', b', l', p', o', i', g', r', q', e'
  22. Dilate(A, n, C) → A''
  23. Dilate(L, n, C) → L'_1
  24. Dilate(P, n, C) → P'_1
  25. Dilate(O, n, C) → O'_1
  26. Dilate(I, n, C) → I'_1
  27. Dilate(G, n, C) → G'_1
  28. Dilate(R, n, C) → R'_1
  29. Dilate(Q, n, C) → Q'_1
  30. Dilate(E, n, C) → E'_1
  31. Dilate(B, n, C) → B''
  32. Polygon(A'', L'_1, P'_1, O'_1, I'_1, G'_1, R'_1, Q'_1, E'_1, B'') → poly9'_1, a'_1, b'_1, l'_1, p'_1, o'_1, i'_1, g'_1, r'_1, q'_1, e'_1

AI Drawing Prompt Reference

Draw an example of polygon dilation (scaling) transformation, showing how polygons enlarge or shrink proportionally about a center point. Start by drawing an original polygon, then create multiple scaled copies around the center point with varying scale factors controlled by a slider. Display corresponding points on lines through the center with distances scaled by the factor. The final image should include the original polygon, scaled copies, and the center point.
The prompt above was compiled from the original drawing commands and is for reference only.