  We prove that if $E \subset {\Bbb F}_q^d$, $d \ge 2$, $F \subset
\operatorname{Graff}(d-1,d)$, the set of affine $d-1$-dimensional planes in
${\Bbb F}_q^d$, then $|\Delta(E,F)| \ge \frac{q}{2}$ if $|E||F|>q^{d+1}$, where
$\Delta(E,F)$ the set of distances from points in $E$ to lines in $F$. In
dimension three and higher this significantly improves the exponent obtained by
Pham, Phuong, Sang, Vinh and Valculescu.
