This construction is in fact used when constructing a line perpendicular to a given line at a given point : drawing a circle whose center is such that it intersects the line in two points , and the perpendicular to be constructed is the one bisecting segment .

Equations

If are the position vectors of two points , then its midpoint is and vector is a normal vector of the perpendicular line segment bisector. Hence its vector equation is . Inserting and expanding the equation leads

1.Previous
3.Next