Question 11The orthocenter of a triangle is the concurrent intersection of the three (possibly extended) altitudes. What is the sum of the coordinates of the orthocenter of the triangle whose vertices are $A(2, 31),$ $B(8, 27),$ and $C(18, 27)?$$5$$17$$10 + 4\sqrt{17} + 2\sqrt{13}$$\dfrac{113}{3}$$54$