Analytical Geometry

$\text{A point on the line }y=-x+6 \text{ is given by }(x, -x+6)\\ \text{the squared distance between two points u and v is given by}\\ d^2(u,v)=(u_x-v_x)^2+(u_y-v_y)^2 \\ \text{if the distance between two points is equal so will the squared distance be, so}\\ d^2[(10,-10),(x,-x+6)] = d^2[(0,0),(x,-x+6)] \\ (10-x)^2 + (-16+x)^2 = x^2 + (-x+6)^2 \\ 2 x^2-52 x+356=2x^2-12 x+36 \\ 320=40x\\ x=8,~y=(-x+6) = -2\\ (x,y) = (8,-2)$

Thank you rom