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

To find the midpoint, use the midpoint formula: \(\displaystyle (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\). Plug in the two ordered pairs to the formula to get: \(\displaystyle (\frac{-10+4}{2},\frac{14+2}{2})\). Doing this will give you a solution of \(\displaystyle (-3,8)\).

The \(\displaystyle x\)-coordinate of the midpoint is 

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

which is negative.

The \(\displaystyle y\)-coordinate of the midpoint is 

\(\displaystyle \frac{-4+10}{2} =3\),

which is positive.

Since the midpoint has a negative \(\displaystyle x\)-coordinate and a positive \(\displaystyle y\)-coordinate, the midpoint is in Quadrant II.

The \(\displaystyle x\)-coordinate of the midpoint is 

\(\displaystyle \frac{5 + (-3) }{2} = 1\),

which is positive.

The \(\displaystyle y\)-coordinate of the midpoint is 

\(\displaystyle \frac{-4+7}{2} = \frac{3}{2}\),

which is positive.

Since both coordinates are positive, the midpoint is in Quadrant I.

To find the midpoint you are actually finding the average of the two \(\displaystyle x\) values and the average of the two \(\displaystyle y\) values. 

Midpoint formula: \(\displaystyle (\frac{x_{1}+x_{2}}{2}), (\frac{y_{1}+y_{2}}{2})\)

\(\displaystyle (-1, 5)\), \(\displaystyle (-7, 3)\) so we plug our points in to the equation, 

\(\displaystyle (\frac{-1+(-7)}{2}, \frac{5+3}{2})\)

Simplify and divide

\(\displaystyle (\frac{-8}{2},\frac{8}{2})\)

Midpoint: \(\displaystyle (-4,4)\)

Use the midpoint formula:

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

Substitute:

\(\displaystyle \frac{x_{1}+x_{2}}{2} =\frac{1.6+(-1.4)}{2} = \frac{0.2}{2} = 0.1\)

\(\displaystyle \frac{y_{1}+y_{2}}{2}} \right = \frac{7.3+4.7)}{2}} = \frac{12}{2} = 6\)

The midpoint is \(\displaystyle (0.1, 6)\)

Use the midpoint formula:

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

Substitute:

\(\displaystyle \frac{x_{1}+x_{2}}{2} = \frac{ \frac{1}{3} + \left (-\frac{5}{6} \right )}{2}= \frac{ \frac{2}{6} - \frac{5}{6} }{2}= \frac{-\frac{3}{6}}{2}= \frac{-\frac{1}{2}}{2} = -\frac{1}{2} \div 2 = -\frac{1}{2} \cdot\frac{1}{2} =-\frac{1}{4}\)

\(\displaystyle \frac{y_{1}+y_{2}}{2} = \frac{ \frac{5}{6} + \frac{2}{3}}{2} = \frac{ \frac{5}{6} + \frac{4}{6}}{2} = \frac{ \frac{9}{6} }{2}= \frac{ \frac{3}{2} }{2} = \frac{3}{2} \div 2 = \frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}\)

The midpoint is \(\displaystyle \left ( -\frac{1 }{4}, \frac{3 }{4} \right )\).

To find the midpoint, you can use the midpoint formula: \(\displaystyle (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\).

Plug in \(\displaystyle (9,-3)\) and \(\displaystyle (-1, 5)\) into the formula: \(\displaystyle (\frac{9+-1}{2},\frac{-3+5}{2})\) to get \(\displaystyle (4,1)\).

Use the midpoint formula:

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

Substitute:

\(\displaystyle \frac{x_{1}+x_{2}}{2} =\frac{3.6+7.2}{2} = \frac{10.8}{2} = 5.4\)

\(\displaystyle \frac{y_{1}+y_{2}}{2}} \right = \frac{9.1+(-1.5)}{2}} = \frac{7.6}{2} = 3.8\)

The midpoint is \(\displaystyle (5.4, 3.8)\)

To find the midpoint of the line, plug the endpoints into the distance formula: \(\displaystyle (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\). This will give you \(\displaystyle (\frac{2+18}{2},\frac{5+-9}{2})\), or a midpoint of \(\displaystyle (10,-2)\).