Let $Q\left(x_{1}, y_{1}\right)$ be the image of the point $P(0,0)$ in the line mirror $4 x+3 y-25=0$. Then, the coordinates of $Q$ are given by
$ \frac{x_{1}-0}{4}=\frac{y_{1}-0}{3}=-\frac{2(4 \times 0+3 \times 0-25)}{25}$
$\Rightarrow \frac{x_{1}}{4}=\frac{y_{1}}{3}=\frac{-2(-25)}{25} \Rightarrow \frac{x_{1}}{4}=\frac{y_{1}}{3}=2$
$\Rightarrow x_{1}=8 \text { or } y_{1}=6 $
Hence, the coordinates of image is $(8,6)$.