1. At what distance from point $A$ on the segment $A B$ should point $K$ be placed so that the sum of the lengths of segments $A K$ and $K B$ is the smallest? The length of segment $A B$ is 9 cm.
1. Since the sum of the lengths of segments $A K$ and $K B$ is always equal to the length of segment $A B$, point $K$ can be any point on segment $A B$.

Answer: at any.