A ray of light passing through the point $(3, 7)$ reflects on the $x-$axis at a point A and the reflected ray passes through the point $(2, 5)$, the coordinates of $A$ are

Let $p$ be the given point $(3, 7)$ and the coordinates of $A$ be $(x, 0)$ so, if the ray $PA$ makes an angle $\theta$ with the positive direction of $x-$axis, the reflected ray $AQ$ , where $Q$ is $(2, 5)$, will make the same angle $q$ with the negative direction of $x-$axis. So the slope of $PA = –$ (the slope of $QA$)
$\begin{array}{l}\Rightarrow \frac{7}{3-x}=-\frac{5}{2-x}\\ \Rightarrow 7(2-x)+5(3-x)=0\\ \Rightarrow x=\frac{29}{12}\end{array}$

$\Rightarrow$  coordinates of $A$ are $\left(\frac{29}{12},0\right).$