# Rotational Transformation

Geometry Level 4

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 $$A + B$$.

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