Question 1100162
Line OM, passing through O (0,0) and M (0,2), is obviously the y-axis.
A line perpendicular to OM would be what we call a horizontal line,
a line with equation y=constant.
If such a line goes through the point  N (3,-1),
it has the equation y=-1.
Line OR, passing through O (0,0) and R (1,1),
obviously has the equation y=x,
and meets the line with equation y=-1 at the point with y=x=-1, point T (-1,-1).
 
The picture below shows, in blue,
triangle OMN, line OM,
the line through the point N, perpendicular to OM,
and point R (circled).
Line OR is shown in red.
 
{{{drawing(300,300,-2,4,-2,4,
grid(1),
blue(line(0,5,0,-3)),blue(line(0,0,0,2)),
blue(line(0,0,3,-1)),blue(line(3,-1,0,2)),
blue(line(-2,-1,4.5,-1)),blue(rectangle(0,-1,0.2,-1.2)),
red(line(-2,-2,4,4)),locate(0.07,-0.05,blue(O)),
locate(0.1,2.3,blue(M)),locate(3.1,-1,blue(N)),
blue(circle(1,1,0.1)),locate(1.15,1.15,blue(R)),
locate(-0.95,-1,T)
)}}}