A rectangular billiard table has vertices at $\mathrm{P}\left(0,0\right),\mathrm{Q}\left(0,7\right),\mathrm{R}\left(10,7\right),$ and $\mathrm{S}\left(10,0\right).$ A small billiard ball starts at $\mathrm{M}\left(3,4\right)$moves in a straight line to the top $\mathrm{M}\left(3,4\right),$ moves in a straight line to the top of the table, bounces to the right side of the table, and then comes to rest at $\mathrm{N}\left(7,1\right)$. The y-coordinate of the point where it is the right side is