**Endpoint Calculator** is a calculator used to help you find the endpoint of any line segment. It’s enough for us to know the starting point and the midpoint for finding an endpoint using our calculator. Once you figure out these two values, make sure to provide them to the calculator, and you wait for the results.

Interestingly, endpoints are not used only in math, but we also can find them and use them for real-life scenarios around us.

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## An endpoint in Geometry – Definition

Before tackling the term “endpoint” and trying to define it properly, we need first to learn what a line segment and a ray are in math.

In mathematics, a line segment is defined as what its name sounds like – a part or a segment of a line. Putting it more formally, a line segment can be described as a line that connects two random points and does not extend past them. On the other hand, we can define a ray as a line that starts at a certain point and extends infinitely in one single direction.

You don’t have to go deep in math to find the representation of line segments. Whenever you look around and spot a line, if you observe a piece of that line between the two distinct points, you can consider it a line segment. Whereas, if you consider a line starting at one point and then continuing infinitely in one direction, we call it a ray.

An endpoint is any point at the end of a line segment or ray in geometry. Endpoints are the points that we can find either on the end of a line segment or one end of a ray. Similarly, in a ray, a line has one endpoint, and the line goes in one direction away from that point and does not extend past that endpoint in the other direction. Therefore, we can think of endpoints as points where a line ends or stops.

## Endpoint Formula

In coordinate geometry, objects are embedded in what we call Euclidean space.

**A little disclaimer:** You don’t have to know or remember the geometric formula of an endpoint. Basically, it’s enough to know that when you say “an endpoint”, we talk about two points, A or B, with coordinates: A = (x₁, y₁) and B = (x₂, y₂).

Let’s imagine that we have a line segment stretching from A = (x₁, y₁) to another definite random point in the space. So, how do we find the endpoint B = (x₂, y₂) if we know the midpoint M = (x, y)?

Putting it in a formula, used in our calculator, the endpoint of any line segment going from A = (x₁, y₁) to a midpoint M = (x, y) is the B = (2x – x₁, 2y – y₁).

**Formula: **

x_{2} = 2x - x_{1}

y_{2} = 2y - y_{1}

## How to Find the Endpoint?

In order to find the endpoint, we need first to have and use some reference point. Then, since we’re dealing with a line segment and its components, we need to figure out what the rest of it looks like.

When we want to find the endpoint, the most common scenario is when we know the starting point and the midpoint. Generally, these two parameters are enough for us to get the endpoint using the endpoint formula. The endpoint must lie at the other end of the midpoint from the starting point and be the same distance away.

Let’s go through the steps for finding an endpoint:

- Draw the line segment that connects the starting point (A) and the midpoint (B)
- Draw a line going from B away from A in an infinite direction
- Measure the distance from points A and B and mark the same distance from B going the other way. The marked point (value) represents the endpoint you seek.

## Endpoint vs. Midpoint

An endpoint differs from a midpoint, but still, we can derive its formula from the midpoint formula. Therefore, we can say that these two geometric terms are fairly close.

By definition, the **midpoint** is a middle point on any line segment. However, not all lines have their midpoints. For instance, a true line in geometry goes infinitely in both directions and cannot have a midpoint.

Similarly, a ray has one endpoint and is infinitely long in the other direction, which means that neither it has nor we can calculate its midpoint. But on the other hand, if we have a line segment with two endpoints, it is possible to calculate its midpoint.

In general, when we have the endpoints of a line segment (x_{1}, y_{1}) and (x_{2}, y_{2}), we can find the coordinates for the midpoint by using the average value of each of the coordinates. The x coordinate of the midpoint is found by adding the two x coordinates, x_{1}, and x_{2}, and dividing them by 2.

Similarly, the y coordinate of the midpoint is found by adding the two y coordinates, y_{1}, and y_{2}, and dividing by 2. This gives us the midpoint formula.

M_{x} = \frac{(x_{1} + x_{2})}{2}

M_{y} = \frac{(y_{1} + y_{2})}{2}

## Endpoint Calculator – Example

It’s important to remember that our Endpoint calculator is not only limited to calculating some geometrical problems. You can use the calculator even for real-world scenarios and problems. We will show you how to use the Endpoint calculator in practice, in the scenario below.

**Scenario:** Let’s assume that you are a business owner, and you want to calculate how much your business will earn in four months. Your current earnings are $35,000, and you’re only three months in the business. How to calculate the earnings in 3 months utilizing the Endpoint calculator?

The starting point was when the moment when you just ran your business, so you were at $0 at that point. Currently, you’re at month three, which is the midpoint. So therefore, using the midpoint, we can find out the endpoint, or in other words, the money we will earn in 4 months.

According to the numbers above, we need both the starting point and the midpoint values to find the answer. Let’s mark them as A = (x₁, y₁) and M = (x, y), respectively. Let’s take the x-axis for the number of months and the y-axis for earnings. Then, we can input those values into the Endpoint calculator as such:

x₁ = 0

x = 3

Now let’s input the parameters for the earnings as such:

y₁ = 0

y = 35,000

Once we provide all this data to the calculator, it will return us the result – our earnings in four months.

x₂ = 6

y₂ = 70,000

So, the Endpoint calculator reports that your business earnings will reach $70,000 in 3 months.

## FAQ

**What is the formula for endpoint?**

When we want to find the endpoint of a line segment, we use the following formula:

x₂ = 2x – x₁

y₂ = 2y – y₁

**How do you find the endpoint in geometry?**

Steps:

– Draw the line segment that connects the starting point (A) and the midpoint (B)

– Draw a line going from B away from A in an infinite direction

– Measure the distance from points A and B and mark the same distance from B going the other way. The marked point represents the endpoint you seek.

Endpoints can be found in an easier way with our Endpoint calculator. Only you have to do is enter the starting and midpoint, and our calculator will do everything else for you.

**How many endpoints does a line have?**

Lines are described as two points, as only a unique line can pass through them. A line has no endpoints, a ray has one endpoint, and a line segment has two endpoints.