  We prove that if a subset of $(\mathbb{F}_q^n)^k$ (with $q$ an odd prime
power) avoids a full-rank three-point pattern
$\vec{x},\vec{x}+M_1\vec{d},\vec{x}+M_2\vec{d}$ then it is exponentially small,
having size at most $3 \cdot c_q^{nk}$ where $0.8414 q \leq c_q \leq 0.9184 q$.
This generalizes a theorem of Kova\u{c} and complements results of Berger, Sah,
Sawhney and Tidor. As a consequence, we prove that if $3$ is a square in
$\mathbb{F}_q$ then subsets of $(\mathbb{F}_q^n)^2$ avoiding equilateral
triangles are exponentially small.
