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Midpoint Formula

Sometimes you will need to find the number that is halfway of two particular numbers. So what do you do? You find the average of the two numbers. In that similar fashion we use the midpoint formula for coordinate geometry to find the halfway number of two coordinates.

midpoint

To find the midpoint of the straight line in a graph, we use this midpoint formula that will enable us to find the coordinates of the end point of the given line. Suppose the endpoints of the line is (x1, y2) and (x2, y2) then the midpoint is given as:

The Midpoint Formula is given as,

\[\large \left(x,y\right)=\left(\frac{x1+x2}{2},\:\frac{y1+y2}{2}\right)\]

Where,
x1, x2 are the co-ordinates of x-axis.
y1, y2 are the co-ordinates of y-axis.

Solved Examples

Question 1: Find the mid point of a line whose end points are (4, 5) and (6, 7)?

Solution:

Given,
(x1,y1) = (4, 5)
(x2,y2) = (6, 7)

According to the formula we can find the midpoint (x, y):

(x, y) =  ($\frac{x_{1}+x_{2}}{2}$,$\frac{y_{1}+y_{2}}{2}$)

(x, y) =  ($\frac{4+5}{2}$,$\frac{6+7}{2}$) = (5, 6)