Proof Writing & Problem Solving · Superchallenge problem

Three frogs sit at lattice points: frog $A$ at $(0, 0)$, frog $B$ at $(1, 0)$, frog $C$ at $(0, 1)$. A move lets one frog jump over another: a frog at $P$ jumps over the frog at $Q$ and lands at $2Q - P$, the reflection of $P$ in $Q$. After some moves, frog $A$ is at $(8, 4)$, frog $B$ is at $(11, 6)$ and frog $C$ is at $(x, 9)$. Find $x$.