초록: In this talk,  we study the cardinality of the distance set determined by a set $A \subset \mathbb F_q^d$  and a set $B$ lying in a $k$-dimensional affine subspace over finite fields. Assuming that the set $B$ lies in a $k$-coordinate plane under translations and rotations, we show that if $|A||B| > 2q^d,$ then $|\Delta(A, B)| > \frac{q}{2},$ where $|\Delta(A, B)|$ denotes the number of elements in the distance set determined by $A$ and $B$. In particular, we show that our result implies the sharp $(d+1)/2$ result for the Erd\H{o}s-Falconer distance problem, where distances are determined by a single set in odd dimensions. Moreover, by another interesting application of our theorem, we improve the results on the Box distance problem by Borges, Iosevich, and Ou.