Problem D

Reflect on This

\(\triangle ABC\) has vertices \(A(2,1)\), \(B(5,8)\), and \(C(1,c)\), where \(c>0\).

Vertices \(A\) and \(B\) are reflected in the \(y\)-axis, and vertex \(C\) is reflected in the \(x\)-axis. The three image points are collinear. That is, a line passes through the three image points.

Determine the coordinates of \(C\).