To drop a perpendicular line from a given point onto a given line using a compass and a straightedge, follow these steps:
- Place the compass at the given point (above or below the line) and adjust its radius to reach the line.
- Draw an arc that intersects the line at two points.
- Without changing the compass setting, place the compass at each of these two intersection points and draw two arcs below (or above) the line, ensuring they intersect.
- Mark the intersection of these arcs—this is the foot of the perpendicular.
- Use a straightedge to draw a line from the given point through this intersection. This is the perpendicular line.
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