AMC 12 2004a Problem 12

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

$\text {(A) } 2 \text {(B) } 2\sqrt2 \text {(C) } 3 \text {(D) } 2 + \sqrt 2 \text {(E) }3\sqrt 2$