Question 1165878
Such point on the line y=x means that vertical and horizontal coordinates are equal.  Distance Formula could help.


{{{(x-6)^2+(y-8)^2=(x-8)^2+(y-0)^2}}}

{{{(x-6)^2+(y-8)^2=(x-8)^2+y^2}}}

and x and y values on that line to be equal,

{{{(x-6)^2+(x-8)^2=(x-8)^2+x^2}}}

{{{(x-6)^2=x^2}}}

{{{x^2-12x+36-x^2=0}}}

{{{36-12x=0}}}

{{{3-x=0}}}

{{{highlight(x=3)}}}--------------and same coordinate value as the one for y.