# Half-Plane

A **half-plane** is one part of a plane divided by a line, referred to as the "half-plane axis" or "origin of the half-plane."

This concept comes from the two-dimensional plane.

For example, if I draw a line on a piece of paper, I create two half-planes: one on the left side of the line and one on the right.

Each half-plane consists of an infinite number of points.

**Note**: Generally, the half-plane includes both the points within one of the regions created by the division and the points on the half-plane axis itself.

## Half-Plane Postulates

A half-plane must satisfy the properties of the **postulate of plane partition by a line**.

Given a line that splits the plane into two sets of points not on the line:

- If we consider any two points P and Q in the same region, the segment connecting them does not intersect the line.

- If we consider any two points P and Q in different regions, the segment connecting them intersects the line.

If a set of points meets this postulate, then it is considered a half-plane.

## Types of Half-Planes

There are two types of half-planes:

**Open Half-Planes**

An open half-plane does not include the dividing line. It consists only of the points inside the half-plane.**Closed Half-Planes**

A closed half-plane includes the dividing line. It consists of both the internal points and the points on the dividing line.

Thus, in the case of a plane divided into two closed half-planes, the points on the half-plane axis are considered to belong to both half-planes.

And so on.