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2016 AMC 10B Question 20

AMC10 · 2016 AMC 10B

Question 20

A dilation of the plane—that is, a size transformation with a positive scale factor—sends the circle of radius $2$ centered at $A(2,2)$ to the circle of radius $3$ centered at $A'(5,6).$ What distance does the origin $O(0,0),$ move under this transformation?
  1. $ \ 0 $
  2. $ \ 3 $
  3. $ \ \sqrt{13} $
  4. $ \ 4 $
  5. $ \ 5 $