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

Perpendicular Bisector

The perpendicular bisector of a line segment is the locus of points on the plane that are equidistant from the endpoints.

Perpendicular Bisector

Perpendicular Bisector

Perpendicular Bisector

Example

Find the equation of the perpendicular bisector of the line segment with endpoints A = (2, 5) and B = (4, −7).

Locus Example

Perpendicular Bisector Calculations

Perpendicular Bisector Calculations

Perpendicular Bisector Solution


Angle Bisectors

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.

Angle Bisectors

Angle Bisectors

Angle Bisectors

Angle Bisectors

Angle Bisectors Formula

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.

Locus Example

Angle Bisector Calculations

Angle Bisector Calculations

Angle Bisector Calculations

Angle Bisector Solution

Angle Bisector Calculations

Angle Bisector Calculations

Angle Bisector Calculations

Angle Bisector Solution

Angle Bisectors


Find the equations of the angle bisectors that form the line r ≡ 3x − 4y + 3 = 0 with the coordinate axes.

Angle Bisector Example

Angle Bisector Calculations

Angle Bisectors

Angle Bisector Calculations

Angle Bisector Calculations

Angle Bisector Solution

Locus Example