Let $A=(9,0)$ and $B=(12,0)$. Points $A^{\prime }$ and $B^{\prime }$ are on the line $y=-x$, and $\overline{A{A}^{\prime }}$ and $\overline{B{B}^{\prime }}$ intersect at $C=(8,2)$. What is the length of $\overline{A^{\prime }{B}^{\prime }}$?