# 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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