# Midpoint Calculator

Midpoint Calculator is an online tool that calculates the midpoint for the given points in a coordinate plane. The midpoint is a point on the line segment that is at an equal distance from the two endpoints. It is also the centroid of the line segment.

## What Is Midpoint Calculator?

Midpoint Calculator is used to compute the midpoint of a line segment when the x and y coordinates of the two endpoints have been specified. The midpoint is a point that divides the line segment internally in a 1:1 ratio. To use the * midpoint calculator* enter the values in the input boxes.

## How to Use the Midpoint Calculator?

Follow these steps to use the online midpoint calculator to find the midpoint of a line segment.

**Step 1:**Go to Ceumath's online midpoint calculator.**Step 2:**Enter the 'x' and 'y' coordinate values for both the points in the respective input boxes.**Step 3:**Click on "**Calculate**" to find the midpoint.**Step 4:**Click on "**Reset**" to clear the fields and enter the new values.

## How Does Midpoint Calculator Work?

The midpoint formula is a special case of the section formula. The section formula is used to determine the ratio in which a point divides a line segment externally or internally. As the midpoint will always divide a line segment in a 1:1 ratio, the section formula can be converted to get the midpoint formula. To find the midpoint of any line segment the following steps are used.

- Take the sum of the two x coordinates of the endpoints and divide it by 2.
- Take the sum of the two y coordinates of the endpoints and divide it by 2.
- The values obtained in step 1 and step 2 will give the x and y coordinates respectively for the midpoint of the line segment.

Given any two points, say A (x_{1}, y_{1}) and C (x_{2}, y_{2}), the midpoint is a point B which is located halfway between points A and C. The formula is given by:

Midpoint = [(x_{1} + x_{2})/2, (y_{1} + y_{2})/2]

## Solved Examples on Midpoint

**Example 1:** Find the midpoint of the line segment joining the points (-3, 2) and (1, -6). Verify this using the midpoint calculator.

**Solution:**

Let (x_{1}, y_{1}) = (-3, 2) and (x_{2}, y_{2}) = (1, -6)

The midpoint is calculated by the formula:

Midpoint = ( (x_{1 }+ x_{2}) / 2 , (y_{1 }+ y_{2}) / 2 )

= ( (-3 + 1) / 2 , (2 + (-6)) / 2 )

= (-2/2 , -4/2)

= (-1, -2)

Therefore, the midpoint of the line segment joining the points (-3, 2) and (1, -6) is (-1, -2)

**Example 2:** Find the midpoint of the line segment joining the points (5, 10) and (3, 12). Verify this using the midpoint calculator

**Solution:**

Let (x_{1}, y_{1}) = 5, 10) and (x_{2}, y_{2}) = (3, 12)

The midpoint is calculated by the formula:

Midpoint = ( (x_{1 }+ x_{2}) / 2 , (y_{1 }+ y_{2}) / 2 )

= ( (5 + 3) / 2 , (10 + 12) / 2 )

= (8/2 , 22/2)

= (4, 11)

Therefore, the midpoint of the line segment joining the points (5, 10) and (3, 12) is (4, 11)

Now use the midpoint calculator to find the midpoint of the line segment joining the following pairs of points.

- (2,3) and (4,5)
- (-4,6) and (-7,-2)

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