# How do you find the midpoint of the line segment joining (4,2) and (8, -1)?

May 17, 2018

$\left(6 , \frac{1}{2}\right)$

#### Explanation:

$\text{given the endpoints of a line segment, say}$

$\left({x}_{1} , {y}_{1}\right) \text{ and } \left({x}_{2} , {y}_{2}\right)$

$\text{then the midpoint is}$

•color(white)(x)[1/2(x_1+x_2),1/2(y_1+y_2)]

$\text{let "(x_1,y_1)=(4,2)" and } \left({x}_{2} , {y}_{2}\right) = \left(8 , - 1\right)$

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

$\textcolor{w h i t e}{\text{midpoint }} = \left[\frac{1}{2} \left(12\right) , \frac{1}{2} \left(1\right)\right] = \left(6 , \frac{1}{2}\right)$