Question

find the midpoint of the line segment with endpoints $left(-\frac{5}{3},\frac{2}{3}
ight)$ and $left(-\frac{7}{3},-\frac{8}{3}
ight)$. the midpoint of the line segment is $square$. (type an ordered pair, using integers or fractions )

Explanation:

Step1: Recall mid - point formula

For two points $(x_1,y_1)$ and $(x_2,y_2)$, the mid - point $(x_m,y_m)$ is given by $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$. Here $x_1=-\frac{5}{3}$, $y_1=\frac{2}{3}$, $x_2=-\frac{7}{3}$, $y_2 =-\frac{8}{3}$.

Step2: Calculate the x - coordinate of the mid - point

$x_m=\frac{-\frac{5}{3}+(-\frac{7}{3})}{2}=\frac{-\frac{5 + 7}{3}}{2}=\frac{-\frac{12}{3}}{2}=\frac{- 4}{2}=-2$.

Step3: Calculate the y - coordinate of the mid - point

$y_m=\frac{\frac{2}{3}+(-\frac{8}{3})}{2}=\frac{\frac{2-8}{3}}{2}=\frac{-\frac{6}{3}}{2}=\frac{-2}{2}=-1$.

Answer:

$(-2,-1)$