constructing a line perpendicular to a line from a given point on the line

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I don't really understand what you're asking, but if you're asking how to do it, then you take your compass, set it to some random length, and take that random length on both sides of the line. Then, at the intersections of the circle that you just drew and the line, take another larger random length, and draw circles where your previous circle intersected the line. Where the last two circles intersected, connect that point with the given point on the line, and there you have it. A line perpendicular to a line from a given poitn on the line.