Education

# What is Section Formula?

Have you heard about the term ‘Coordinates’? A point that denoted the exact position of a known variable is known as Coordinates. The process of finding these coordinates which divide a segment of line either externally or internally into any ratio can be defined as the section formula. The applications of section formula range from the excentres and incenters of a triangle to the equilibrium and the value of the center of mass, (Both the physical and mathematical world). This formula is also used to calculate or find the middlemost point which is also known as the midpoint of a line segment. In this article, we will try to cover some basic concepts regarding the section formula such as the internal section formula external section formula, midpoint formula, and do a brief analysis about these topics.

## What Do You Mean by Midpoint Formula?

In mathematics, the midpoint can be defined as the middlemost point of a straight line. For example, if there are three points in a line segment such as A, B, and C where A and B are the initial and terminal points respectively, the midpoint is denoted by B. The formula to calculate the midpoint of a line segment can be regarded as the midpoint formula. If you find the middlemost point of a line, you may observe that the midpoint has divided the line into two equal halves. The other use of the midpoint formula is to calculate or find the exact position of the points at the end. The formula was given to find the midpoint is, ½ of the sum of coordinates of x variable and ½ of the sum of coordinates of y variable.

In the next few sections, we may try to cover some examples related to the midpoint formula so that you grasp the topic conceptually.

## Some Examples Related to Midpoint Formula

As mentioned above, the formula to calculate the midpoint of a line segment can be regarded as the midpoint formula. Let us now solve some questions about the midpoint formula.

Example 1: Using the formula of the midpoint, calculate the middlemost point of the coordinates, X (5,3 ) and Y which is equivalent to ( 7,8 ).

Solution: Given that,

Coordinates of X = 5 and 3

Coordinates of Y = 7 and 8

Using the midpoint formula,

X = 5 + 7 /2 = 12 / 2 = 6

Y = 3 + 8 /2 = 11 / 2

Therefore, the midpoint of the coordinates X and Y are 6 and 11/2 respectively.

Example 2: Using the formula of the midpoint, calculate the middlemost point of the coordinates, X (4, 2 ) and Y which is equivalent to ( 8, 6 ).

Solution: Given that,

Coordinates of X = 4 and 2

Coordinates of Y = 8 and 6

Using the midpoint formula,

X = 4 + 8 /2 = 12 / 2 = 6

Y = 2 + 6 /2 = 8 / 2 = 4

Therefore, the midpoint of the coordinates X and Y are 6 and 4 respectively.

## Internal And External Section Formula

In the paragraph mentioned above, we came to know that the process of finding these coordinates which divide a segment of line either externally or internally into any ratio can be defined as the section formula. The formula for the internal part is generally used when the segment of the line is divided into ratios in the internal portion. Here, AB: PB.  The formula for the external part is generally used when the segment of the line is divided into ratios in the external portion. You may find in the formula that, x and y are the points, n and m are the differentiating ratios.

If you want to learn about section and midpoint formulas in a detailed, fun, and interactive manner, visit the Cuemath website.