Perpendicular From a Point Off a Line

This construction creates a perpendicular from a point that does not lie on the line. It is used for spacing, alignment, and establishing clean vertical or horizontal references in geometric layouts.

By drawing an arc from the off‑line point that intersects the line twice, you create two equal distances. Those equal distances become the centres for arcs that define the perpendicular.

Step‑by‑Step Construction

• To construct a line from Point C that is perpendicular to the line A-B.
• Place the compass point on C, the point off the line.
• Draw an arc that cuts the line at two points (A and B).
• From A and B, draw arcs of equal radius so they cross.
• Connect the crossing point to P with a straightedge.
• This new line is perpendicular to the original line.

Notes

• The first arc from P must be large enough to reach the line.
• The two intersection points A and B must be used as centres.
• The arcs from A and B must be drawn with the same radius.