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If there is no centre of enlargement then just draw the octagon with each side three times as long.

If there is a centre of enlargement:

  1. join each vertex to the centre;
  2. measure the distance from the centre to the vertex;
  3. triple this measurement;
  4. plot the vertex at this length along the line from the centre that passes through the vertex;
  5. join the vertices of the new octagon which were joined in the original octagon.
Step 2 and 3 are easier if done by considering the x and y movements separately; for example if the centre is at (1, 2) and a vertex is at (3, 5), then the distance between the centre and the vertex is (3-1, 5-2) = (2, 3); tripling this gives (2×3, 3×3) = (6, 9), so the corresponding vertex of the new octagon would be at (1+6, 2+9) = (7, 11)
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Q: The regular octagon shown is enlarged so that its side are 3 times as large?
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