Question

Let \(A=(-6,3), B=(2,7)\), and \(C\) be the vertices of a triangle. Say the altitudes through the vertices \(A\) and \(B\) intersect at \(Q=(2,-1)\). Find the coordinates of \(C\).

[The altitude through a vertex of a triangle is a straight line through the vertex that is perpendicular to the opposite side - or an extension of the opposite side. Although not needed here, the three altitudes always intersect in a single point, sometimes called the orthocenter of the triangle.]