History

Locus ideas emerged from classical compass-and-straightedge geometry and later became a core part of analytic geometry and optimization problems.

Checkpoints

Describe the locus of points 5 cm from point \(A\).

Answer: A circle center \(A\), radius 5 cm.

What is locus of points equidistant from \(A\) and \(B\)?

Answer: Perpendicular bisector of segment \(AB\).

Points within 2 m of line \(l\): describe region.

Answer: Strip between two parallels 2 m from \(l\), including boundaries if “within or equal to”.

Points equidistant from intersecting lines \(p,q\): what locus?

Answer: The two angle bisectors of lines \(p,q\).

Why can a locus answer be a region instead of a curve?

Answer: Inequality conditions describe many points satisfying a distance range.

Applications

• Cell/Wi-Fi planning: coverage zones around transmitters.
• Urban design: buffer distances from roads or facilities.
• Robotics: safe navigation boundaries and target zones.

References

• Standard high-school geometry content on loci and construction.
• Analytic geometry materials linking loci to equations.