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 \(\displaystyle (3,3)\).