Let $A=(10,-10)$ and $O=(0,0).$ Determine the sum of all $x$ and $y-$coordinates of all points $Q$ on the line $y=-x+6$ such that $\angle OQA = 90^\circ.$
Using the perpendicular condition, the only point that works is (4,2), so the answer is 4 + 2 = 6.
