# How do you find the midpoint of ( 3, 8 ) and ( 5, 4 )?

May 24, 2018

$\left(4 , 6\right)$

#### Explanation:

$\text{given coordinates of endpoints say}$

x_1,y_1)" and "(x_2,y_2)" then"

$\text{midpoint } = \left[\frac{1}{2} \left({x}_{1} + {x}_{2}\right) , \frac{1}{2} \left({y}_{1} + {y}_{2}\right)\right]$

$\text{let "(x_1,y_1)=(3,8)" and } \left({x}_{2} , {y}_{2}\right) = \left(5 , 4\right)$

$\text{midpoint } = \left[\frac{1}{2} \left(3 + 5\right) , \frac{1}{2} \left(8 + 4\right)\right]$

$\textcolor{w h i t e}{\text{midpoint }} = \left(4 , 6\right)$

May 24, 2018

The midpoint equal:
$M = \left({x}_{\text{midpoint"),y_("midpoint}}\right) = \left(4 , 6\right)$

#### Explanation:

Let ;

$A = \left({x}_{1} , {y}_{1}\right) = \left(3 , 8\right)$

$B = \left({x}_{2} , {y}_{2}\right) = \left(5 , 4\right)$

To find the ${x}_{\text{midpoint}}$

${x}_{\text{midpoint}} = \frac{{x}_{1} + {x}_{2}}{2} = \frac{3 + 5}{2} = \frac{8}{2} = 4$

To find the ${y}_{\text{midpoint}}$

${y}_{\text{midpoint}} = \frac{{y}_{1} + {y}_{2}}{2} = \frac{8 + 4}{2} = \frac{12}{2} = 6$

The midpoint equal:

$M = \left({x}_{\text{midpoint"),y_("midpoint}}\right) = \left(4 , 6\right)$

Show the sketch below: