Question 1100162: The vertices of the triangle OMN are the point O (0,0), M (0,2), N (3,-1) and the point R (1,1). The line through the point N, perpendicular to OM, meets OR produced at T. Find the coordinates of T.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 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.
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