Locus
A locus is a set of points that satisfy a certain condition or criteria.
The criteria that defines the locus has to be translated to an algebraic language in order to solve problems involving types of locus.
Examples of Locus
Perpendicular Bisector
The perpendicular bisector of a line segment is the locus of points on the plane that are equidistant from the endpoints.
Example
Find the equation of the perpendicular bisector of the line segment with endpoints A = (2, 5) and B = (4, −7).
Angle Bisectors
The bisector of an angle is the locus of points on the plane that are equidistant from the rays that form the angle.
The two angle bisectors are perpendicular between themselves.
Examples
Find the equations of the angle bisectors which determine the lines r ≡ 3x − 4y + 5 = 0 and s ≡ 6x + 8y + 1 = 0.
Find the equations of the angle bisectors that form the line r ≡ 3x − 4y + 3 = 0 with the coordinate axes.
