As the name implies midpoint values refers to the middle or center point somewhere, however, in geometry the midpoint specifically refers to the midpoint of a line segment.
The midpoint of a line segment is a point that is present exactly in the middle of that line segment, i.e. at an equal distance from both the endpoints. The midpoint of any line segment is calculated using the midpoint formula.
This article focuses on concepts of the midpoint, like what is midpoint, how to calculate the midpoint using the midpoint formula, and the difference between the midpoint and the endpoint.
Table of Contents
The midpoint is a specific point present o a line segment that divides it into two equal lengths. As per the definition of midpoint, it is the point on a line segment having endpoints A and B, present exactly in the center of those endpoints A and B.
That means the midpoint of a line segment is always present at the same distance from point A as from point B. Accordingly, it can be said that the midpoint can be calculated by taking the mean or average of both the length of the endpoint.
The midpoint formula is an equation that is used to calculate the midpoint of a line segment or the distance from any endpoint to the midpoint. In terms of geometry, the midpoint formula determines the distance between two known coordinate coordinates that is midway between the two positions.
Calculating the midpoint between endpoints using the midpoint formula is just a matter of calculating the average of the endpoint values. In fact, the average, or mean of the endpoint values is calculated using the midpoint formula.
This formula is frequently used in conjunction with maps and the distance formula. The midpoint formula is frequently used to determine the midpoint of a line segment in order to bisect it. Another application is to demonstrate that a line segment has been bisected.
However, in the coordinate plane only when the two endpoints on a graph are known, the midpoint formula cold be utilized to calculate the midpoint formula. The midpoint or M of the two endpoints (x1, y1) and (x2, y2) is calculated as
M = (x1+ x2/ 2, y1+ y2 / 2)
How to Calculate Midpoint
To calculate the midpoint as mentioned above the midpoint formula is implied. If in a line segment having the two endpoints (x1,y2) and (x1,y2) they are calculated as (x1+ x2/ 2, y1+ y2 / 2).
This means by simply taking the average of both the coordinates we can calculate the midpoint between them. The average is the arithmetic mean that is calculated by simply adding the values and then dividing the sum by the total number of values. You can also try the midpoint formula calculator to do this online.
Therefore by taking the averages of the x and y values of both the coordinates the midpoint formula is implemented.
Mean of x coordinates
The first step in this regard is, taking the mean of the x coordinates i.e. x1 + x2 / 2. Thus we have to add the values given for the x coordinates then divide their sum by 2.
Mean of y coordinates
Just the same way average of x coordinates’ values is calculated, the mean of the values for y coordinates is calculated. For instance, the values of y1 and y2 are added up and then divided by 2.
The resultant mean values of both the coordinates provide the midpoint calculation of the line segment.
Difference Between Midpoint and Endpoint
The midpoint and endpoint both are components of a line segment however, there are huge differences among both parts. The midpoint of a line segment as discussed above is the point present exactly in the center of it while the endpoints are the points present on the extreme ends of the line segment.
Moreover, the endpoint could be found on both ends of a line segment as well as on one end of a ray while the endpoint is specifically present in the middle of a line segment.
The midpoint is at the equal difference from both endpoints of a line segment, on the other hand, the calculation for endpoints varies from one type to another. Using the midpoint formula, the endpoint formula can be derived successfully, that aids in finding the values of endpoints.
According to the endpoint formula, the endpoint of a line segment is calculated by putting other endpoint’s and midpoint’s values in the formula.
The midpoint is the point present precisely in the center of the line segment and cuts it into two equal parts. The midpoint is calculated using the midpoint formula that is simply the averages of both coordinates.
Other than the midpoint, a line segment consists of two endpoints as well. The endpoints formula is calculated through derivation from midpoint formulas. In other words, the midpoint formula is required to calculate the endpoints of a line segment.