Task 563

The task

The diagram shows 28 lattice points, each one unit from its nearest neighbors. Segment $AB$ meets segment $CD$ at $E$. Find the length of segment $AE$. [asy] unitsize(0.8cm); for (int i=0; i<7; ++i) { for (int j=0; j<4; ++j) { dot((i,j)); };} label("$A$",(0,3),W); label("$B$",(6,0),E); label("$D$",(2,0),S); label("$E$",(3.4,1.3),S); dot((3.4,1.3)); label("$C$",(4,2),N); draw((0,3)--(6,0),linewidth(0.7)); draw((2,0)--(4,2),linewidth(0.7)); [/asy]