# How do you find the midpoint of (5 1/2, -4 1/4), (3 3/4, -1 1/4)?

Jan 12, 2017

See the full process for finding the midpoint below:

#### Explanation:

First, convert all of the mixed fractions to improper fractions over the same common denominator:

(((4/4xx5) + (2/2 xx 1/2)), ((4/4 xx -4) - 1/4)) and

(((4/4 xx 3) + 3/4), ((4/4 xx -1) - 1/4))

((20/4 + 2/4), (-16/4 - 1/4)) and

((12/4 + 3/4), (-4/4 - 1/4))

(22/4, -17/4) and (15/4, -5/4)

We can now use the midpoint formula to find the midpoint of these two points.

The formula to find the mid-point of a line segment give the two end points is:

$M = \left(\frac{\textcolor{red}{{x}_{1}} + \textcolor{b l u e}{{x}_{2}}}{2} , \frac{\textcolor{red}{{y}_{1}} + \textcolor{b l u e}{{y}_{2}}}{2}\right)$

Where $M$ is the midpoint and the given points are:

$\textcolor{red}{\left({x}_{1} , {y}_{1}\right)}$ and $\textcolor{b l u e}{\left({x}_{2} , {y}_{2}\right)}$

Substituting the points from our problem gives:

$M = \left(\frac{\textcolor{red}{\frac{22}{4}} + \textcolor{b l u e}{\frac{15}{4}}}{2} , \frac{\textcolor{red}{- \frac{17}{4}} + \textcolor{b l u e}{- \frac{5}{4}}}{2}\right)$

$M = \left(\frac{\frac{37}{4}}{2} , \frac{- \frac{22}{4}}{2}\right)$

$M = \left(\frac{37}{8} , - \frac{22}{8}\right)$

$M = \left(4 \frac{5}{8} , - 2 \frac{6}{8}\right)$

$M = \left(4 \frac{5}{8} , - 2 \frac{3}{4}\right)$