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≥13 is 3q-4 and describe all resolving sets of that size if q≥ 23. The metric dimension of a biaffine plane (also called a flag-type elliptic semiplane) of order q≥ 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≥ 7, and to 3q-9√(q) under

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... n 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≥2, is at least {6q-27,4q-7}, while for the classical generalized quadrangles W(q) and Q(4,q) it is at most 8q.