Question 946466
Let the x and y axes be the two perpendicular lines.
Then the distance from the origin will be the distance from the perpendicular lines. 
So then the sum of the distances would be {{{x+y=1}}}.
So in the first quadrant, the locus of points would look like a straight line with points (0,1) and (1,0). 
In the second quadrant it would contain (0,1) and (-1,0).
Third quadrant (-1,0) and (0,-1).
and finally in the fourth quadrant (0,-1) and (1,0). 
When you put it all together, it would be a square rotated 45 degrees about the origin, the length of the side of the square would be {{{s=sqrt(2)}}}.
{{{drawing(300,300,-3,3,-3,3,grid(1),circle(0,1,0.1),circle(0,-1,0.1),circle(-1,0,.1),circle(1,0,0.1),blue(line(0,1,1,0)),blue(line(1,0,0,-1)),blue(line(0,-1,-1,0)),blue(line(-1,0,0,1)))}}}