Cartesian plane challenge

Geometry Level 5

In the Cartesian plane, \(\triangle ABC (\angle A=90^{\circ})\), \(K\) is an inversion point of \(A\) through \(C\), the line pass \(K\) perpendicular to \(BC\) at \(E\) and cut \(AB\) at \(N(-1;3)\). Let \(\angle AEB=45^{\circ}\), \((BK): 3x+y-15=0\), \(y_B>3\). Find the sum of the coordinates of vertices \(A,B,C\).

Submit your answer to 3 decimal places.

Clarification: The sum of the coordinates is \(x_A+y_A+x_B+y_B+x_C+y_C\).

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