Cartesian plane challenge 2Geometry Level 5
In \(\triangle ABC\), let \((AH):x+y-6=0\) be the perpendicular (\(H\in BC\)), \((BE): x-2y+1=0\) and \((CK): x-1=0\) are the medians (\(E\in AC; K\in AB\)). Find the coordinates of vertices \(A,B\) and \(C\). Submit your answer as their sum (to 2 decimal places).
- The sum is \(x_A+y_A+x_B+y_B+x_C+y_C\)