How to Calculate Midpoint Values Step by Step?

As you can make a guess from the name, midpoint, it is a point present between two points. For numbers, it is a number between two numbers.

By combining both the numbers and by dividing them into two, i.e., the mean of both numbers, you can have the midpoint.

But how can you calculate the midpoint of a line segment?

One thing to be considered regarding the midpoint, it is always of a line segment. A ray and a simple line that goes infinitely in both directions cannot have a midpoint, only a line segment having two endpoints can have a midpoint.

Sometimes students confuses the concept of midpoint with significant figures and combination values. These are all different concepts in algebra. 

Midpoint

A point present just between two points and the center of the line segment connecting them is the midpoint.

The midpoint can be defined according to Euclidean geometry as a point present on the line segment that is equidistant from its both endpoints.

The midpoint is in the exact center and equidistant from the two points of the line segment. For instance, with two points, A and C, the point B present exactly in the midway between A and C is the midpoint.

However, the end points of the line are the reference points, between these two points is present the midpoint.

The midpoint splits the line between the two points in two equal parts. Moreover, the line passes through the midpoint when a line is drawn to bisect the line segment having two endpoints.

Midpoint Formula

The midpoint formula depends on taking the x-coordinates and the y-coordinates average. It is used to identify the midpoint coordinates of an x-y plane in a line segment.

This means that the two x-values’ and two y-values’ average formulates midpoint formula.

In fact, we have to calculate the average or mean of the x coordinates and y-coordinates separately while calculating the midpoint coordinates of each segment.

For all kinds of line segments including vertical, horizontal and even diagonal, the midpoint formula is used to find its midpoint.

Moreover, an ordered pair is found by using the midpoint formula. The midpoint formula has enormous geometry application.

Given below is the formula used for calculating the midpoint of a line segment, however, this formula is only for a segment in 2D plane.

(x,y) = (x₁+x₂/2),(y₁+y₂/2)

Calculating Midpoint Step by Step

After you have grasped a brief concept of the midpoint present on a line segment, now move towards the basic part of our article, calculating the midpoint.

So let's calculate the midpoint of a line segment, consider the step by step procedure provided below.

1. Utilize Midpoint formula

   To utilize the midpoint formula in order to calculate the midpoint of a line segment the coordinates of endpoints must be present.

   Thus, first of all, the coordinates for which both the points and the midpoint of a section must be found, should be provided. 

2. Remove the x coordinates

   Then, we will first remove the x coordinates to obtain the x-coordinate midpoint. For instance, the value for x coordinates is 2 and 6, thus we remove 2 and 6 from A and B.

   Just sum up these two values, and divide by 2 for average. Now, this is the midpoint (6+2 = 4) for the first value.

3. Remove the y coordinates

   Then the same step is repeated for y-coordinates to get its midpoint. For y coordinates suppose we have 4 and 6, respectively for the points A and B again.

   After summing them together gives us 10, and then after dividing by 2 the answer will be 5.

4. Use of Midpoint equation

   We found that, using the midpoint equation, the midpoint between the two points is precisely at the coordinates 4 and 5 according to the midpoint rule.

   You'll notice, in fact, that this is the point that splits the segment into two equal sections if you plot the segment in a graph and then drop a point on 4 and 5.

We learn above that the midpoint of a line segment is just the middle point present between the two endpoints of the segment.

For a line segment having two endpoints, the midpoint can be calculated by finding the average or mean of both end point’s coordinates separately.

Therefore, by using the midpoint formula, we can calculate it by first taking coordinates (x, y) average of the first end point and then of the second point.

Simply taking the average of the endpoint's coordinates, the midpoint can be calculated.