By using the midpoint formula, we can find the x and y coodinantes fo the midpoint.

$\displaystyle midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$\displaystyle \frac{x_1+x_2}{2}=\frac{2+4}{2}=\frac{6}{2}=3$

$\displaystyle \frac{y_1+y_2}{2}=\frac{3+1}{2}=\frac{4}{2}=2$

Our coordinates are (3, 2).

To find the midpoint of a line segment, you add together the $\displaystyle x$ components and divide by two ($\displaystyle \frac{2+8}{2}$ = 5) , do the same for $\displaystyle y$ ($\displaystyle \frac{3+9}{2}$ =6). The answer is (5, 6).

To find the midpoint we must know the midpoint formula which is  

$\displaystyle (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

We then take the $\displaystyle x$-coordinate from the first point and plug it into the formula as $\displaystyle x_{1}$.

We take the $\displaystyle x$-coordinate from the second point and plug it into the formula as $\displaystyle x_{2}$.

We then do the same for $\displaystyle y_{1}$ and $\displaystyle y_{2}$.

With all of the points plugged in our equation will look like this. 

$\displaystyle (\frac{3+9}{2},\frac{12+15}{2})$

We then perform the necessary addition and division to get the answer of 

$\displaystyle (\frac{12}{2},\frac{27}{2})=(6,13.5)$

The average of the the $\displaystyle x$-coordinates and the average of the y-coordinates of the given points will give you the mid-point of the line that connects the points. 

$\displaystyle \textup{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$, where $\displaystyle (x_1,y_1)$ is $\displaystyle (0,-3)$ and $\displaystyle (x_2,y_2)$ is $\displaystyle (-2, 4)$.

$\displaystyle (\frac{(0)+(-2)}{2}, \frac{(-3)+(4)}{2})$

$\displaystyle (\frac{-2}{2},\frac{1}{2})$

$\displaystyle (-1, \frac{1}{2})$

The midpoint formula is $\displaystyle \left ( \frac{x_{1} + x_{2}}{}2, \frac{y_{1} + y_{2}}{2}\right)$.

When we plug in our points, we get $\displaystyle \left ( \frac{14}{2}, \frac{-4}{2}\right)$.

So, our final answer is $\displaystyle (7,-2)$.

The length to the midpoint is the difference between the two points divided by two.  That number must then be added to the point:

$\displaystyle X_{midpoint}=X_{1}+\frac{\left (X_{2}-X_{1} \right )}{2}=2+\frac{\left (8-2 \right )}{2}=2+\frac{6}{2}=2+3=5$

$\displaystyle Y_{midpoint}=Y_{1}+\frac{\left (Y_{2}-Y_{1} \right )}{2}=4+\frac{\left (28-4 \right )}{2}=4+\frac{24}{2}=4+12=16$

The difference in $\displaystyle x$-values is 14 and the difference in $\displaystyle y$-values is 8.  The midpoint therefore differs by values of 7 and 4 from either of the endpoints.

$\displaystyle \textup{The coordinates of the midpoint are the averages of the other points' coordinates.}$

$\displaystyle x\textup{-coordinate}=\frac{5+\left ( -3)\right )}{2}=1\;\;\;\;y\textup{-coordinate}=\frac{2+10}{2}=6$

$\displaystyle \textup{The midpoint is at }\left (1,6\right )$

The midpoint formula is $\displaystyle (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

To find the midpoint of $\displaystyle (5,-2)$ and $\displaystyle (-1,0)$, you simply plug in the points into the midpoint formula: $\displaystyle (\frac{5+-1}{2},\frac{-2+0}{2})$, which gives you the point $\displaystyle (2,-1)$.

You can find the midpoint of the line by using the midpoint formula: $\displaystyle (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$. Plug the endpoints into the formula to get $\displaystyle (\frac{10+-4}{2},\frac{{-2}+8}{2})$, or $\displaystyle (3,3)$.