G.3.1 Learning Goals
- I can understand and apply the terms scale factor and dialtion.
- I can dilate a figure given a scale factor and center.
Glossary
Scale factor is the number by which every length in an original figure is multiplied when you make a scaled copy.
A dilation with center P and positive scale factor k takes a point A along the ray PA to another point whose disctance is k times furthere away from P than A is.
![](data:image/png;base64,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)