Construct the line perpendicular to Modifying above NO with bar at point P.
A line segment is labeled with points N, P, and O from left to right.
To construct a line perpendicular to the given line segment NO at point P, follow these steps:
1. Place the point of the compass on point P.
2. Adjust the compass to a moderate width—its exact size doesn't matter, as long as it's wide enough to intersect the line segment NO on both sides of point P.
3. Swing an arc above and below the line segment NO, so that it intersects the line at two points, which we can call A and B. These intersecting points should be on opposite sides of point P and on the line segment NO.
4. Keeping the same compass width, place the point of the compass on point A and draw an arc above or below the line (in the area where you want the perpendicular line to be).
5. Without changing the width of the compass again, place the point of the compass on point B and draw another arc that intersects the first arc drawn in step 4. The intersection of the two arcs is a new point, which we can call C.
6. Now, use a straightedge to draw a line from point P through the intersection point C. This new line PC will be perpendicular to the line segment NO, crossing it at a 90-degree angle at point P.
The resulting PC is the perpendicular line to NO at point P.