Dilations, Area, and Perimeter

The sketch below shows two triangles related by a dilation. Be certain to drag the vertices around and drag point D around so you get a feel for how this transformation works! Be certain to explore different values for the scale factor! Be certain to drag point D inside the two triangles! Be certain to put point D at the vertex of one of the triangles! Be certain to put point D on the edge of one of the triangles!

  1. Which triangle is the PRE-IMAGE?
  2. Which triangle is the IMAGE?
  3. Which point is the CENTER OF DILATION?
  4. What is the SCALE FACTOR?
  5. Which area relationship gives the scale factor?
  6. Why are the incorrect area relationships incorrect?
  7. Why is the perimeter relationship correct?
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Steve Phelps, Created with GeoGebra