Where to Build the Roads

Chef bought a huge (effectively infinite) planar island and built $N$ restaurants (numbered $1$ through $N$) on it. For each valid $i$, the Cartesian coordinates of restaurant $i$ are $(X_i, Y_i)$. Now, Chef wants to build $N-1$ straight narrow roads (line segments) on the island. The roads may have arbitrary lengths; restaurants do not have to lie on the roads. The slope of each road must be $1$