Perpendicular Line

Perpendicular Bisector
1. Begin with a line segment $$\overline{A B}$$

2. Construct two circles, $$\overset{\frown}{A B}$$ and $$\overset{\frown}{B A}$$. They intersect and points C and D.

3. Line $$\overset{\longleftrightarrow}{C D}$$ is perpendicular to $$\overline{A B}$$ and intersects it at its midpoint, M.

AlDraw also has a shortcut for finding perpendicular bisectors. It is under the "Shortcuts" menu, and its hotkey is alt-3.

Perpendicular Line through a Point on a Line
1. Begin with a line and a point P on that line.

2. Construct an arbitrary circle, centered on P. It intersects the line at points A and B.

3. Construct the perpendicular bisector of A and B.

This can also be done in AlDraw using the Tangent Line shortcut.

Perpendicular Line through a Point not on a Line
1. Begin with a line and a point not on that line.

2. Construct an arbitrary circle large enough to intersect the line. It intersects at points A and B.

3. Construct the perpendicular bisector of A and B.