Use the midpoint formula:

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

$\displaystyle \small mid=(\frac{-5+3}{2},\frac{-3+7}{2})$

$\displaystyle \small mid=(\frac{-2}{2},\frac{4}{2})$

$\displaystyle \small mid=(-1,2)$

Repeated application of the midpoint formula $\displaystyle \left (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2} \right )$ yields the following:

Since $\displaystyle B$ is the midpoint of $\displaystyle \overline{AC}$, substitute the coordinates of $\displaystyle A$ for $\displaystyle x_{1}$ and $\displaystyle y_{1}$, set equal to the coordinates of $\displaystyle B$, and solve as follows:

$\displaystyle 7 = \frac{3+x_{2}}{2}$

$\displaystyle 14 =3+x_{2}$

$\displaystyle x_{2} = 11$

$\displaystyle -1= \frac{7+y_{2}}{2}$

$\displaystyle -2= 7+y_{2}$

$\displaystyle -9= y_{2}$

$\displaystyle C$ is the point $\displaystyle (11, -9)$.

We can find the coordinates of $\displaystyle D$ similarly using those of $\displaystyle A$ and $\displaystyle C$:

$\displaystyle 11= \frac{3+x_{2}}{2}$

$\displaystyle 22 = 3+x_{2}$

$\displaystyle 19= x_{2}$

$\displaystyle -9= \frac{7+y_{2}}{2}$

$\displaystyle -18= 7+y_{2}$

$\displaystyle -25= y_{2}$

$\displaystyle D$ is the point $\displaystyle (19, -25)$

Repeated application of the midpoint formula, $\displaystyle \left (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2} \right )$, yields the following:

$\displaystyle A$ is the point $\displaystyle (8,1)$ and $\displaystyle D$ is the point $\displaystyle \left (1, 9 \right )$. $\displaystyle C$ is the midpoint of $\displaystyle \overline{AD}$, so $\displaystyle C$ has coordinates

$\displaystyle \left (\frac{8+1}{2}, \frac{1+9}{2} \right )$, or $\displaystyle \left ( 4.5, 5\right )$.

 $\displaystyle B$ is the midpoint of $\displaystyle \overline{AC}$, so $\displaystyle B$ has coordinates

$\displaystyle \left (\frac{8+4.5}{2}, \frac{1+5}{2} \right )$, or $\displaystyle (6.25, 3)$.

$\displaystyle E$ is the midpoint of $\displaystyle \overline{BD}$, so $\displaystyle E$ has coordinates

$\displaystyle \left (\frac{6.25+1}{2}, \frac{3+9}{2} \right )$, or $\displaystyle (3.625, 6)$.

Write the formula to find the midpoint.

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

Substitute the points into the equation.

$\displaystyle M = (\frac{2+1}{2}, \frac{6+(-9)}{2})$

The midpoint is located at:  $\displaystyle (\frac{3}{2}, -\frac{3}{2})$

The answer is:  $\displaystyle (\frac{3}{2}, -\frac{3}{2})$

Write the formula for the midpoint.

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

Substitute the points.

$\displaystyle M=(\frac{1+(-2)}{2},\frac{7+(-6)}{2}) = (\frac{-1}{2}, \frac{1}{2})$

The answer is:  $\displaystyle (-\frac{1}{2}, \frac{1}{2})$

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Based on your data, you know that your midpoint could be calculated as follows:

$\displaystyle (\frac{4-7}{2},\frac{5+10}{2})=(\frac{-3}{2},\frac{15}{2})$

This is the same as:

$\displaystyle (-1.5,7.5)$

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Based on your data, you know that your midpoint could be calculated as follows:

$\displaystyle (\frac{-10-22}{2},\frac{4-4}{2})=(\frac{-32}{2},\frac{0}{2})$

This is the same as:

$\displaystyle (-16,0)$

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Now, you can write your data out as follows, as you know the midpoint value as well as one of the values for your end points:

$\displaystyle (0,5)=(\frac{84+x_2}{2},\frac{1+y_2}{2})$

To finish solving, think of it like two different equations:

$\displaystyle \frac{84+x_2}{2}=0$ 

and

$\displaystyle \frac{1+y_2}{2}=5$

Now, solve each for the respective values:

$\displaystyle 84+x_2=0$

$\displaystyle x_2=-84$

and

$\displaystyle 1+y_2=10$

$\displaystyle y_2=9$

Therefore, your other point is $\displaystyle (x_2,y_2)$ or $\displaystyle (-84,9)$

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Now, you can write your data out as follows, as you know the midpoint value as well as one of the values for your end points:

$\displaystyle (-10,-22)=(\frac{-2+x_2}{2},\frac{-7+y_2}{2})$

To finish solving, think of it like two different equations:

$\displaystyle \frac{-2+x_2}{2}=-10$ 

and

$\displaystyle \frac{-7+y_2}{2}=-22$

Now, solve each for the respective values:

$\displaystyle -2+x_2=-20$

$\displaystyle x_2=-18$

and

$\displaystyle -7+y_2=-44$

$\displaystyle y_2=-37$

Therefore, your other point is $\displaystyle (x_2,y_2)$ or $\displaystyle (-18,-37)$

To find the midpoint between two points, we will use the following formula:

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

where $\displaystyle (x_1,x_2)$ and $\displaystyle (y_1,y_2)$ are the given points.

So, given the points

$\displaystyle (8,2)$ and $\displaystyle (10,4)$, we can substitute into the formula. We get

$\displaystyle M = (\frac{8+10}{2}, \frac{2+4}{2})$

$\displaystyle M = (\frac{18}{2}, \frac{6}{2})$

$\displaystyle M = (9,3)$