find the midpoint of the line segment with endpoints $\left(-\frac{2}{3},\frac{1}{3}\
ight)$ and $\left(-\frac{16}{3},-\frac{13}{3}\
ight)$. the midpoint of the line segment is $\square$. (type an ordered pair, using integers or fractions.)

Question

Accepted Answer

# Explanation:
## Step1: Find the x - coordinate of the midpoint
The formula for the x - coordinate of the midpoint $M_x$ of two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M_x=\frac{x_1 + x_2}{2}$.
Here $x_1=-\frac{2}{3}$, $x_2 =-\frac{16}{3}$.
$$
\begin{align*}
M_x&=\frac{-\frac{2}{3}+(-\frac{16}{3})}{2}\
&=\frac{-\frac{2 + 16}{3}}{2}\
&=\frac{-\frac{18}{3}}{2}\
&=\frac{- 6}{2}\
&=-3
\end{align*}
$$
## Step2: Find the y - coordinate of the midpoint
The formula for the y - coordinate of the midpoint $M_y$ of two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M_y=\frac{y_1 + y_2}{2}$.
Here $y_1=\frac{1}{3}$, $y_2=-\frac{13}{3}$.
$$
\begin{align*}
M_y&=\frac{\frac{1}{3}+(-\frac{13}{3})}{2}\
&=\frac{\frac{1-13}{3}}{2}\
&=\frac{-\frac{12}{3}}{2}\
&=\frac{-4}{2}\
&=-2
\end{align*}
$$

# Answer:
$(-3,-2)$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find the x - coordinate of the midpoint

Step2: Find the y - coordinate of the midpoint

Answer: