Rotational Transformation

Geometry Level 4


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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