Midpoint Formula – Definition & Formula

In mathematics, the midpoint is defined as the point in the middle of a straight line. For example, if a line segment has three points: A, B, and C, where A and B are the starting and terminal points, respectively, the midway is represented by B. The midpoint formula is the formula for calculating the midpoint of a line segment. If you discover the midpoint of a line, you will notice that it has divided the line into two equal halves. The midpoint formula may also be used to calculate or identify the precise position of the points at the finish.

Midpoint Formula

To calculate the midpoint of any given line, let’s say for example line AB, how would you find the midpoint of the line AB? The formula to calculate the midpoint requires the coordinates of line AB, 

Coordinates of A = (x,y)

Coordinates of B = (u,v)

Midpoint formula = ((x+u)/2, (y+v)/2)

Example – The coordinates of point A is (2,4) and the coordinates of point B are (6,8). What is the midpoint of line AB?

Using the formula and substituting the values, we get {(2+6)/2} = 4 & {(4+8)/2} = 6

The coordinate of the midpoint is (4,6).

Formulas Concerning the Midpoint

The midpoint formula contains separate computations for the x-coordinate and y-coordinate of the coordinates or points. Furthermore, the calculations of points between two provided points include a comparable computation of the given points’ x-coordinate and y-coordinate. The midpoint formula is closely connected to the following two formulae.

1. Section Formula 
2. The formula for Centroid of Triangle

Important Midpoint Remarks

The main qualities of the midpoints are as follows.

1. A line segment is divided in an equal ratio by the midpoint, which is 1:1.
2. A line segment is divided into two equal halves by the midway.
3. A line segment’s bisector cuts it at its midway.

Questions & Solution

Example 1: Using the formula of the midpoint, calculate the midpoint of the coordinates, X ( 6, 2 ) and Y which is equivalent to ( 4, 6 ).

Solution: Let’s note that all the information given in the question,

Coordinates of X = (6,2)

Coordinates of Y = (4,6)

Using the midpoint formula, 

X = 6 + 4 /2 = 10 / 2 which equals 5

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

Therefore, the midpoint of the coordinates X and Y are 5 and 4 respectively. 

Example 2: Calculate the midpoint of the coordinates, A ( 1, 2 ) and B which is equivalent to ( 3, 4 ).

Solution: Let’s note that all the information given in the question,

Coordinates of point A = (1,2)

Coordinates of point B = (3,4)

Using the midpoint formula discussed above, 

A = 1 + 3 /2 = 4 / 2 which equals 2

B = 2 + 4 /2 = 6 / 2 which equals 3

Therefore, the midpoint of the coordinates A and B are 2 and 3 respectively. 

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