The perpendicular bisector of a line divides the line into two equal segments and is perpendicular to the line
The perpendicular distance of point P from the line l is equal to the distance of the lost point s from the line l and points P and s are on opposite sides of the line l
The point s can be marked by constructing the perpendicular to line l passing through P
The steps to construct a perpendicular line from a point to a line and mark point s are given as follows;
- Place the compass at the point P, and draw an arc intersecting line l at two points, A and B
- Place the compass at point A and draw an arc with a radius, r, larger than half the length of segment AB above and below line l
- Place the compass point at point B, and with the same radius r draw arcs intersecting the the arcs drawn from point A above and below the line
- Mark the point of intersection of the two arcs above and below the line l as the points D and E
- Join points D and E with the a line to form the line DE drawn with a straightedge and extend DE line such that it passes through point P
- Mark the point of intersection of the line DE and line l as the point F on the line l
- Place the compass at the point F, and with a radius FP, draw an arc to intersect the line DE on the other side of the line l
- Mark the point of intersection of the line DE by the arc of radius FP as the point s
The constructed point s above is the required point and points P and s are located on opposite sides of the line l
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