Understanding Loci Basics

What is a Locus?

A locus (plural: loci) is a set of points that satisfy a certain condition or rule. In geometry, it often describes the path or area that a point can occupy based on specific constraints.

For example:

• The locus of points equidistant from a single point forms a circle.
• The locus of points equidistant from two points forms the perpendicular bisector of the segment connecting the two points.

Common Loci in Plane Geometry

• Circle: The set of all points equidistant from a fixed point (the center).
• Perpendicular Bisector: The set of all points equidistant from two given points.
• Angle Bisector: The set of all points equidistant from the sides of an angle.

Finding the Locus of a Point

To find the locus of a point, follow these steps:

1. Identify the Condition: Determine the rule or condition that defines the locus.
2. Apply the Condition: Use geometric principles to find the path or area that satisfies the condition.
3. Draw the Locus: Represent the locus on a graph or diagram.

 

Examples

Example 1: Locus of Points Equidistant from Two Points

Problem: Find the locus of points equidistant from points A and B.

 

Example 2: Locus of Points a Fixed Distance from a Point

Problem: Find the locus of points 5 cm from point P.