# Midpoint calculator | Midpoint of a line segment calculator

## Midpoint calculator

Endpoint1 ⇒   x1:   ,   y1:

Endpoint2 ⇒   x2:   ,   y2:

With our easy-to-use midpoint calculator, you can quickly find the middle point between any two given points on a plane. Simply enter the coordinates of the two points (x1, y1) and (x2, y2) and hit “Calculate” to get the step-by-step solution and a graphical representation of the three points. It’s that simple! Try it out now and save time on your calculations.

## Definition of a midpoint in geometry

In geometry, a midpoint is the point that divides a line segment into two equal parts. It is located at the exact center of the segment and is equidistant from both endpoints. The midpoint formula is used to calculate the coordinates of the midpoint of a line segment, given the coordinates of its endpoints.

## What is the midpoint formula?

The midpoint formula of a segment is derived from the coordinates of its endpoints. To obtain the midpoint, add the x-coordinates of the endpoints and divide the sum by two. Similarly, add the y-coordinates of the endpoints and divide the sum by two. This will give you the coordinates of the midpoint.

Therefore, if we have the points A and B with coordinates A=(x1,y1) and B=(x2,y2), the formula for the midpoint is:

### Midpoint formula

M(xm,ym) = ( x1+x22 , y1+y22 )

## How to find the midpoint of a line segment

To find the midpoint of a line segment, you can follow these steps:

1. Locate the coordinates of the endpoints of the line segment. Let’s say the coordinates of the endpoints are A=(x1,y1) and B=(x2,y2).
2. Use the midpoint formula to calculate the midpoint.
M(xm,ym) = ( x1+x22 , y1+y22 )
This formula finds the average of the x-coordinates and the average of the y-coordinates of the endpoints.
3. Simplify the formula by plugging in the values of x1, x2, y1, and y2 to find the coordinates of the midpoint.
4. The result will be the coordinates of the midpoint of the line segment.

## Midpoint examples

In this section, we will explore some examples of how to use the midpoint formula to find the midpoint of a line segment or other geometric shapes. These examples will demonstrate how the midpoint formula can be used in various real-life situations.

Example 1: Finding the midpoint of two buildings

Suppose you are an architect designing a plaza, and you need to find the midpoint between two buildings. The first building is located at coordinates (10, 20), and the second building is located at coordinates (30, 40). To find the midpoint, you can use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((10 + 30)/2, (20 + 40)/2)

Midpoint = (20, 30)

So the midpoint between the two buildings is (20, 30).

Example 2: Finding the midpoint of a room

Suppose you are designing a room that is 12 feet wide and 16 feet long. To find the midpoint of the room, you can use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((0 + 12)/2, (0 + 16)/2)

Midpoint = (6, 8)

So the midpoint of the room is (6, 8), which is the center of the room.