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A line is the most fundamental concept in geometry as most figures are based on it. There are various types of lines that have specific properties and uses. One such type of line is a half line.

A half line is a term used in analytical geometry. Let’s understand what is half line in geometry and its properties.

## What is Analytical Geometry?

Before understanding what is half line in geometry, let’s understand what is analytical geometry. Analytical geometry is that branch of Algebra in which the position of the point on the plane can be located using an ordered pair of numbers called Coordinates. This is also called coordinate geometry or Cartesian geometry.

Analytical geometry contradicts synthetic geometry, where there is no use of coordinates or formulas. It is considered an axiom or assumption, to solve the problems. But analytical geometry, it defines the geometrical objects using the local coordinates. It also uses algebra to define this geometry.

## Line in Analytical Geometry

In analytical geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it.

## What is Half Line in Geometry?

A half line is a term related to analytical geometry. A half line is a straight line extending from a point infinitely in only one direction. A half line is a kind of line segment that only extends in a single direction and is terminated in the other direction. A ray can also be called a half line in mathematics, specifically in the analytical geometry branch. The half line is denoted as:

A half line is a part of a line consisting of the given point and all the points lying on one of the sides of it. Any point on a line divides it into two half lines.

**Note:** A half line is called a ray in geometry.

## Naming a Half Line in Geometry

On its way to infinity, a half line may pass through more than one point. A half line is named using its initial point and any other point through which it passes. So, the first letter of a half line’s name indicates its starting point.

When naming a half line, it is denoted by drawing a small half line on top of the name of the half line.

The figure above represents a half line AB. Here, the starting point of half line AB is A, and on its way to infinity, it passes through point B.

Now consider the diagram below. It has a half line that passes through two points on its endless journey. The starting point of this half line is P. You can name it half line PQ or half line PR.

## Properties of a Half Line

Following are the properties of a half line

- A half line is a geometric figure that has no height or width. It only has an indefinite length.
- The name of a half line must always include its origin point.
- We need two half lines to form an angle.

## Differentiate Between Half Line and Ray in Geometry

The terms half line and ray are the same. Both are used to represent a part of a line that has a beginning point and no endpoint.

In analytic geometry, a part of a line starting from a point but not having an endpoint is called a half line, whereas in geometry it is called a ray.

## Practice Problems

- What is half line?
- What is the difference between geometry and analytical geometry?
- What is the difference between half line and ray?

## FAQs

### Is half-line a ray?

The terms half line and ray are the same. Both are used to represent a part of a line that has a beginning point and no endpoint.

### What is the difference between ray and half line?

There is no difference between ray and half line. In analytic geometry, a part of a line starting from a point but not having an endpoint is called a half line, whereas in geometry it is called a ray.

### What is a semi line in math?

A straight line extends infinitely in a single direction from a point.

## Conclusion

In this article we understood what is half line in geometry. A half line is a term related to analytical geometry. A half line is a straight line extending from a point infinitely in only one direction. A half line is a kind of line segment that only extends in a single direction and is terminated in the other direction.