Question 191
In the plane, the two points are considered. $P(8,2)$ y $Q(5,11)$. A mobile moves from $P$ a $Q$ according to a path that must meet the following conditions: The mobile starts from $P$ and reaches a point on the axis $x$, along which runs a segment of length $1$; Then it separates from this axis and goes towards a point on the axis $y$, on which a segment of length travels $2$; separates from the axis $y$ finally and goes to the point $Q$. Among all possible paths, determine the minimum length, as well as this same length.