<s>[INST] A particle moves from point $A$ at the origin $(0,0)$ of a coordinate system to point $B$ at $(24, 18)$.  Then the particle moves from $B$ to point $C$, which is at $(12, 30)$.  In this case the distance traveled is the sum of the distance from $A$ to $B$ and the distance from $B$ to $C$.
 If another point $D$ is to be chosen so that the distance from $A$ to $D$, where $D$ can be anywhere in the plane, is as close as possible to the distance from $A$ to $B$ plus the distance from $B$ to $C$, what should be the coordinates of point $D$?[/INST]