  We count the $\mathbb{F}_q$-rational points of GIT quotients of quiver
representations with relations. We focus on two types of algebras -- one is
one-point extended from a quiver $Q$, and the other is the Dynkin $A_2$
tensored with $Q$. For both, we obtain explicit formulas. We study when they
are polynomial-count. We follow the similar line as in the first paper but
algebraic manipulations in Hall algebra will be replaced by corresponding
geometric constructions.
