The midpoint is given by taking the mean, or average, of the \(\displaystyle x\) and \(\displaystyle y\) coordinates separately.

Let \(\displaystyle P_{1}=\left ( 7,5 \right )\) and \(\displaystyle P_{2} = \left (-1,3 \right )\)

So the midpoint formula becomes \(\displaystyle \frac{x_{1}\ +\ x_{2}}{2}= \frac{7-1}{2}=3\) and \(\displaystyle \frac{y_{1}+y_{2}}{2}= \frac{-5 +3}{2}=-1\)

So the midpoint is \(\displaystyle (3,-1)\)

Use the midpoint formula:

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

\(\displaystyle (\frac{-5+(-3)}{2}, \frac{6+2}{2})=(\frac{-8}{2}, \frac{8}{2})=(-4,4)\)

The midpoint formula is as follows:

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

This makes sense; it is as simple as the average of the \(\displaystyle x\) and \(\displaystyle y\) components of each point.

For this problem, \(\displaystyle x_1=-3,x_2=-1,y_1=-3,and\: y_2=1\).

So the midpoint is \(\displaystyle \left ( -2,-1 \right )\)

The distance formula is as follows:

\(\displaystyle distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The order you put the first and second components of each point does NOT matter, when a positive or negative number is squared, it will always come out positive.        

\(\displaystyle (2)^2=4\; and\; (-4)^2=16\)

So the distance is \(\displaystyle \sqrt{(-3+1)^2+(-3-1)^2} =\sqrt{4+16}=\sqrt{20}=2\sqrt{5}\)

To find the midpoint of a line segment, you must find the mean of the x values and the mean of the y values.

Our x values are \(\displaystyle -2\) and \(\displaystyle -6\) to find their mean, we do \(\displaystyle (-2+-6)/2=-4\).

Our y values are \(\displaystyle -9\) and \(\displaystyle -1\), so our mean is \(\displaystyle (-9+-1)/2=-5\). Therefore, our midpoint must be \(\displaystyle (-4,-5)\).

The coordinate of the midpoint of the line segment connecting a pair of points is

\(\displaystyle \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

So for the pair of points \(\displaystyle (x_1,y_1)=(2,2)\) and \(\displaystyle (x_2,y_2)=(4,12)\),

we get:

\(\displaystyle \left(\frac{2+4}{2}, \frac{2+12}{2}\right)=(3, 7)\)

The coordinate of the midpoint of the line segment connecting a pair of points is

\(\displaystyle \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\).

So for the pair of points \(\displaystyle (x_1,y_1)=(0, 0)\) and \(\displaystyle (x_2,y_2)=(8, 0)\)

we get,

\(\displaystyle \left(\frac{0+8}{2}, \frac{0+0}{2}\right)=(4, 0)\)

The origin is the point \(\displaystyle \small (0,0)\). We can use the regular midpoint formula with \(\displaystyle \small (0,0)\) as \(\displaystyle \small (x_{1}, y_{1})\) and the given point \(\displaystyle \small (14, -2)\) as \(\displaystyle \small (x_{2}, y_{2})\):

\(\displaystyle \small (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

\(\displaystyle \small (\frac{0+14}{2} , \frac{0+-2}{2})\)

\(\displaystyle \small (\frac{14}{2}, \frac{-2}{2}) = (7, -1)\)

Note that since the first point is the origin, we're averaging these points with 0, or in other words just dividing by 2.

To find the mid-point given two points on the coordinate plane you are basically finding the average of the x-values and the average of the y-values.  To do this follow the formula below:

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

With our points this gives:

\(\displaystyle \Big( \frac{5+3}{2} \; , \frac{10+6}{2} \Big )\)

The midpoint is the point that is equidistant from each endpoint point.

We find it using a formula that computes the average of the x and y coordinates.

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

\(\displaystyle \left(\frac{4+(-6)}{2},\frac{5+8}{2}\right)\)

\(\displaystyle \left(\frac{-2}{2},\frac{13}{2}\right)\)

\(\displaystyle \mathbf{\left(-1,\frac{13}{2}\right)}\)

Recall the formula for finding a midpoint of a line segment:

\(\displaystyle \text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

\(\displaystyle \text{Midpoint}=(\frac{2+1}{2}, \frac{4+8}{2})=(\frac{3}{2}, 6)\)