AMC 12 2007a Problem 13

A piece of cheese is located at $(12,10)$ in a coordinate plane. A mouse is at $(4,-2)$ and is running up the line $y=-5x+18$. At the point $(a,b)$ the mouse starts getting farther from the cheese rather than closer to it. What is $a+b$?

$\mathrm{(A)}\ 6 \mathrm{(B)}\ 10 \mathrm{(C)}\ 14 \mathrm{(D)}\ 18 \mathrm{(E)}\ 22$