MathDB
Dilation Of The Plane

Source: Problem #20 2016 AMC 10B

February 21, 2016
AMC10AMCAMC 10circles2016 AMC 10B

Problem Statement

A dilation of the plane—that is, a size transformation with a positive scale factor—sends the circle of radius 22 centered at A(2,2)A(2,2) to the circle of radius 33 centered at A(5,6)A’(5,6). What distance does the origin O(0,0)O(0,0), move under this transformation?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 13<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> 5<span class='latex-bold'>(A)</span>\ 0\qquad<span class='latex-bold'>(B)</span>\ 3\qquad<span class='latex-bold'>(C)</span>\ \sqrt{13}\qquad<span class='latex-bold'>(D)</span>\ 4\qquad<span class='latex-bold'>(E)</span>\ 5