Difference between revisions of "1999 AIME Problems/Problem 6"

Revision as of 19:54, 10 March 2007

Problem

A transformation of the first quadrant of the coordinate plane maps each point $\displaystyle (x,y)$ to the point $\displaystyle (\sqrt{x},\sqrt{y}).$ The vertices of quadrilateral $\displaystyle ABCD$ are $\displaystyle A=(900,300), B=(1800,600), C=(600,1800),$ and $\displaystyle D=(300,900).$ Let $\displaystyle k_{}$ be the area of the region enclosed by the image of quadrilateral $\displaystyle ABCD.$ Find the greatest integer that does not exceed $\displaystyle k_{}.$