Question 1011469
They would be either or both of two parallel lines to y=x.


Pick any convenient point on the line y=x, and find the line perpendicular to y=x at that point; find the equation for this perpendicular line.  Try point (1,1) on y=x.  The perpendicular line is {{{y-1=-(x-1)}}},
{{{y=-x+1+1}}}
{{{y=-x+2}}}


This perpendicular line is a general point  (x, -x+2).
You want distance from (x, -x+2)  to  (1,1)  to be square-root of 2.
Use the distance formula.


Do you find a pathway to continue and finish?