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Dilation Transformation Demo by robertcartwright (2)

Dilation Transformation Demo by robertcartwright (2)
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2018-02-17 01:52
PolygonCoordinate GeometryMatrixTransformationGeometric Construction
This example demonstrates the dilation transformation of a polygon in a plane, where polygon S is scaled by a factor d centered at point D to produce a new polygon S'. It involves core mathematical concepts such as transformation, matrix, properties of similar figures, and central symmetry. The construction uses GeoGebra commands like Polygon and Dilate, with objects including S, D, C, A, B, E, F, G, H, I, J, K, L, M, poly1, d, e, f, g, h, i, j, k, l, m, E', F', G', H', I', J', K', L', M', D', poly1', d', e', f', g', h', i', j', k', l', m'. Suitable for high school students to learn the geometric meaning of dilation transformations and the application of matrices in geometry.

GeoGebra Commands & Parameters

  1. Polygon(D, E, F, G, H, I, J, K, L, M) → poly1, d, m, e, f, g, h, i, j, k, l
  2. Dilate(E, S, C) → E'
  3. Dilate(F, S, C) → F'
  4. Dilate(G, S, C) → G'
  5. Dilate(H, S, C) → H'
  6. Dilate(I, S, C) → I'
  7. Dilate(J, S, C) → J'
  8. Dilate(K, S, C) → K'
  9. Dilate(L, S, C) → L'
  10. Dilate(M, S, C) → M'
  11. Dilate(D, S, C) → D'
  12. Polygon(D', E', F', G', H', I', J', K', L', M') → poly1', d', m', e', f', g', h', i', j', k', l'

AI Drawing Prompt Reference

Draw a polygon S, then scale it by a factor of d centered at point C to create a new polygon S'. First, draw polygon S, then sequentially scale its vertices E, F, G, H, I, J, K, L, M to get E', F', G', H', I', J', K', L', M'. Finally, scale the center point D of S by C to get D', and use these points to draw the new polygon S'.
The prompt above was compiled from the original drawing commands and is for reference only.