Rotational Transformation

Consider

A square $ABCD$ with coordinates $(0,0), (0,a), (a,a)$ and $(a,0)$ .

A point $P$ with coordinates $(0,-a)$ .

And a line $l$ with inclination $\frac{1}{6}$ and $y$ -intercept $\frac{-7 a}{3}$ .

Find coordinates of two points $x_{1}$ and $x_{2}$ along the edges of square such that the line segments from these points to line $l$ have the midpoint $P$ .

If the distance between $x_{1}$ and $x_{2}$ can be expressed as $\frac{\sqrt{A}\: a}{B}$ then find $A + B$ .