Cartesian plane challenge 2

Geometry 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).

Clarification

  • The sum is \(x_A+y_A+x_B+y_B+x_C+y_C\)
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