# How do you find the midpoint of (5,-2), (3,-6)?

Apr 23, 2017

See the entire solution process below:

#### Explanation:

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:

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

Substituting the values from the points in the problem gives:

$M = \left(\frac{\textcolor{red}{5} + \textcolor{b l u e}{3}}{2} , \frac{\textcolor{red}{- 2} + \textcolor{b l u e}{- 6}}{2}\right)$

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

$M = \left(4 , - 4\right)$

Apr 23, 2017

$\left(4 , 2\right)$

#### Explanation:

The midpoint of a segment with endpoints:

$A = \left({x}_{1} , {y}_{1}\right) \mathmr{and} B = \left({x}_{2} , {y}_{2}\right)$ has coordinates :

$\left[\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right]$

So in this case the midpoint is:

$\left[\frac{5 + 3}{2} , \frac{- 2 - \left(- 6\right)}{2}\right]$ => simplify:

$\left[\frac{8}{2} , \frac{- 2 + 6}{2}\right]$

$\left(4 , 2\right)$

Apr 23, 2017

The midpoint of (5 , -2), (3 , -6) is (4 , -4)

#### Explanation:

The midpoint formula is $\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

${x}_{1}$ = 5 because your first point on "x" is 5 from (5,-2)

${x}_{2}$ = 3 because your second point on "x" is 3 from (3,-6)

${y}_{1}$ = -2 because your first point on "y" is -2 from (5,-2)

${y}_{2}$ = -6 because your second point on "y" is -6 from (3,-6)

From here all you need to do is substitute values.

$\left(\frac{\left(5\right) + \left(3\right)}{2} , \frac{\left(- 2\right) + \left(- 6\right)}{2}\right)$

$\left(\frac{5 + 3}{2} , \frac{- 2 - 6}{2}\right)$

$\left(\frac{8}{2} , \frac{- 8}{2}\right)$ [Simplify your fractions by dividing]

(4 , -4)

To get a better understanding of this formula, remember that any number divided by 2 is the middle of that number. So what we are doing here is adding our points together and then dividing them by 2.
Here's a simple example:

What is the midpoint between (20 , 0) and (10 , 0)?

All I have to do is 20 + 10 = 30

and then divide by 2

$30 \div 2 = 15$

(15 , 0)

I know this is the right answer because I can add and subtract the same number from my midpoint to return to my two original points. In this case that number is 5.

15 + 5 = 20

15 - 5 = 10