The midpoint is the point at the same distance between 2 ends of a line. The midpoint calculator helps you to find the equidistance from two specified endpoints on a line by taking two coordinates in the cartesian coordinate system, with endpoints as A and B.

## What Is the Midpoint?

**A particular point that lies at the center of a line segment is known as the midpoint.**

The midpoint divides the line segment into two parts of the same length. It lies in between two reference points that make up a line.

## Midpoint Formula:

$$ (x_{M}, y_{M}) = \left(\dfrac {x_{1} + x_{2}} {2} , \dfrac {y_{1} + y_{2}} {2}\right) $$

**Where:**

(x1, y1) _ First endpoint of a line segment

(x2, y2) _ Second endpoint of a line segment

## How To Find the Midpoint Between Two Points?

When you are given any two points of a bar, you can find the midpoint by hand.

- Add the X coordinate values and determine their half (Divide by 2)
- Repeat the same procedure for the Y coordinate of the midpoint

## How To Find the Midpoint With Two Endpoints?

By using the endpoints evaluate the midpoint by following the steps below:

**Step # 1: Consider the midpoint formula**

$$ M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right) $$

**Step # 2: Separate the equations for both X and Y coordinates**

$$ x_{M} = \dfrac {x_{1} + x_{2}} {2} $$

$$ y_{M} = \dfrac {y_{1} + y_{2}} {2} $$

**Step # 3: Rearrange both equations to solve for X and Y **

$$ x_{2} = 2x_{M} - x_{1} $$

$$ y_{2} = 2y_{M} - y_{1} $$

### Practical Example:

Let’s make a supposition that you have two endpoints A and B. So, calculate the midpoint of a line given 2 endpoints. These points have the coordinates as follows:

$$ A = \left(2, 8\right) $$

$$ B = \left(3, 6\right) $$

#### Solution:

$$ M = (x_M, \; y_M) $$

$$ M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right) $$

$$ M = \left(\dfrac{2 + 3}{2}, \; \dfrac{8 + 6}{2}\right) $$

$$ M = \left(\dfrac{5}{2}, \; \dfrac{14}{2}\right) $$

$$ M = \left(2\dfrac{1}{2}, \; 7\right) $$

$$ M = (2.5, \; 7) $$

## Instructions For Using This Calculator:

The midpoint calculator allows you to calculate the midpoint of the line segment by using the following guide:

### Input Values:

- Enter the X coordinates and Y coordinates using numbers,
__fractions__, mixed numbers, or decimals - Tap on "Calculate"

### Output Summary:

- Midpoint of a line segment with stepwise calculations
- Decimal approximation, difference, and ratio
- Percent increase and arithmetic comparison
- Number line and Pie chart
- Vector length with possible intermediate steps
- Angles between vector and coordinate axes
- Polar coordinates

## How to Find The Distance Between Two Points?

To discover the point that lies exactly between 2 coordinates, use the distance and midpoint calculator. This helps you to determine the distance between 2 points on a horizontal or vertical line.

The following formula can be used to calculate the distance between two endpoints of a line segment:

$$ d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} $$

- Determine the coordinates of both points
- Put these coordinate values into the distance formula
- Find the square root after simplifying the expressions

## Additional Queries:

### How To Find the Midpoint of a Triangle?

The midpoint of the triangle is known as Centroid and can be calculated as:

- Determine the midpoints of all 3 sides
- Using the endpoint and midpoint of all sides, sketch bars that intersect the triangle sides from the center
- Where the edges meet, that is the midpoint of the triangle

### What Is The Midpoint of (0,2) and (2,8)?

The midpoint between (0, 2) and (2, 8) is;

= (1, 5)

### Do You Round Midpoints?

The midpoint can not be rounded off.

## References:

**Wikipedia:** Midpoint, Construction, Geometric properties involving midpoints, Generalizations

**Khan Academy:** Midpoint formula, Distance between points

**Lumen Learning:** Calculating Price Elasticities Using the Midpoint Formula, Midpoint Method, Distance Formula, The Standard Form Of Equations Of Circles