Loci

Locus

8.1

Locus

Definition

A trace or trajectory formed by a set of points in a plane or three-dimensional space satisfies certain conditions.

The shapes of two-dimensional loci can be seen in the form of straight lines, arcs and curves.

Example

The following diagram shows a pole \(MN\) and a board \(PQRS\).

\(PQRS\) is attached to \(MN\) to make it movable.

If the side \(PQ\) is rotated \(360{^\circ}\) around \(MN\), what is the three-dimensional shape formed?

The shape formed when the side \(PQ\) is rotated \(360{^\circ}\) around \(MN\) is a right cylinder.

Cylinders, spheres, cones, prisms and pyramids are examples of three-dimensional shapes.