jmc

Note that the reflecting over itself results in itself, so $$\left(\begin{array}{cc}-\frac{7}{25}& \frac{24}{25}\\ \frac{24}{25}& \frac{7}{25}\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}x\\ y\end{array}\right).$$Then $-\frac{7}{25}x+\frac{24}{25}y=x$ and $\frac{24}{25}x+\frac{7}{25}y=y.$ Both equations lead to $\frac{y}{x}=\boxed{\frac{4}{3}}.$