  In this paper the metric dimension of (the incidence graphs of) particular
partial linear spaces is considered. We prove that the metric dimension of an
affine plane of order $q\geq13$ is $3q-4$ and describe all resolving sets of
that size if $q\geq 23$. The metric dimension of a biaffine plane (also called
a flag-type elliptic semiplane) of order $q\geq 4$ is shown to fall between
$2q-2$ and $3q-6$, while for Desarguesian biaffine planes the lower bound is
improved to $8q/3-7$ under $q\geq 7$, and to $3q-9\sqrt{q}$ under certain
stronger restrictions on $q$. We determine the metric dimension of generalized
quadrangles of order $(s,1)$, $s$ arbitrary. We derive that the metric
dimension of generalized quadrangles of order $(q,q)$, $q\geq2$, is at least
$\max\{6q-27,4q-7\}$, while for the classical generalized quadrangles $W(q)$
and $Q(4,q)$ it is at most $8q$.
