Endpoint — Definition, Formula & Examples

An endpoint is a point at which a line segment ends or a ray starts. Every line segment has exactly two endpoints, and every ray has exactly one.

An endpoint is a point that marks a boundary of a line segment or the initial point of a ray. A line segment $\overline{AB}$ is the set of all points between $A$ and $B$ , inclusive of both endpoints $A$ and $B$ . A ray $\overrightarrow{AB}$ begins at endpoint $A$ and extends infinitely through $B$ .

How It Works

To identify endpoints, look for where a figure starts or stops. A line segment

\overline{PQ}

has two endpoints,

P

and

Q

, so it has a definite length. A ray

\overrightarrow{PQ}

has one endpoint at

P

and extends forever past

Q

, so it has no measurable length. A full line has no endpoints at all — it extends infinitely in both directions. When two rays share the same endpoint, that shared point is called the vertex of an angle.

Worked Example

Problem: A line segment has endpoints at

A(1, 3)

and

B(5, 3)

. What is the length of the segment?

Identify the endpoints: The two endpoints are

A(1, 3)

and

B(5, 3)

. Since they share the same

y

-coordinate, the segment is horizontal.

Find the distance: Subtract the

x

-coordinates to find the length.

|5 - 1| = 4

Answer: The length of

\overline{AB}

is 4 units.

Why It Matters

Endpoints define the boundaries you work with when measuring segments, naming angles, or plotting figures on a coordinate plane. In any geometry course, correctly identifying endpoints is essential for applying the distance formula, naming rays, and finding angle vertices.

Common Mistakes

Mistake: Thinking a ray has two endpoints.

Correction: A ray has only one endpoint (its starting point) and extends infinitely in one direction. A line segment is the figure with two endpoints.