# Midpoint Formula

The midpoint formula is used to determine the point that is exactly halfway between two given points in a coordinate plane (the midpoint). Thus, a midpoint divides a line segment into 2 equal halves.

If A and B are two points with coordinates (x1, y1) and  (x2, y2), respectively, their midpoint can be found by the formula:

${\left( \dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\right)}$

Thus, the distance formula calculates the average of the given point’s x- and y-coordinates.

## Finding Midpoint Formula

Let us plot the points A (x1, y1) and B (x2, y2) on the coordinate plane.

By joining the points ‘A’ and ‘B,’ we get a line segment AB. The midpoint of AB is the point halfway between A and B, so the point is M.

Here, the expression for the x-coordinate of the midpoint is ${\dfrac{x_{1}+x_{2}}{2}}$, which is the average of the x-coordinates. Similarly, the expression for the y-coordinate of the midpoint is ${\dfrac{y_{1}+y_{2}}{2}}$}}$, which is the average of the y-coordinates. Thus, the midpoint is: M =${\left( \dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\right)}$Find the midpoint of the two points, A (7, 9) and B (2, 5), using the midpoint formula. Solution: Given (x1, y1) = (7, 9), the coordinates of the first point (x2, y2) = (2, 5), the coordinates of the second point Now, applying the formula, we get${\left( \dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\right)}$=${\left( \dfrac{7+2}{2},\dfrac{9+5}{2}\right)}$=${\left( \dfrac{9}{2},\dfrac{14}{2}\right)}$=${\left( \dfrac{9}{2},7\right)}$or${\left( 4.5,7\right)}$Thus, the midpoint between the points A (7, 9) and B (2, 5) is${\left( \dfrac{9}{2},7\right)}$or${\left( 4.5,7\right)}$The endpoints of a line segment are (p, 5) and (6, 15). If the midpoint is (2, 10), find the value of p. Solution: Given (x1, y1) = (p, 5) and (x2, y2) = (6, 15) As we know, the midpoint is${\left( \dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\right)}$Here,${\left( \dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\right)}$= (2, 10) Comparing the x-coordinates,${\dfrac{x_{1}+x_{2}}{2}}$= 2 ⇒${\dfrac{p+6}{2}}\$ = 2
⇒ p = -2
Thus, the value of p is -2