Locus

This is a locust, a kind of grasshopper.

It has nothing at all to do with a locus except that locus and locust sound the same.

A locus is a set of points that satisfy certain rules.

For example, a locus of points that are a fixed distance from a central point describes a circle.

What does the locus of points that are a fixed distance from a line look like?

The outer shape is the locus of points a fixed distance from the line

What about the locus of points the same distance from two lines that meet to form an angle?

This is the angle bisector

What about the locus of points the same distance, or equidistant, from two points?

This is the perpendicular bisector