Answer
The value of the length and the midpoint of the line segment whose endpoints are $\underline{5}$ and $\underline{\left( \frac{7}{2},0 \right)}$ respectively.
Work Step by Step
Calculate the length of the line segment as follows:
$\begin{align}
& d=\sqrt{{{\left( 5-2 \right)}^{2}}+{{\left( 2-\left( -2 \right) \right)}^{2}}} \\
& =\sqrt{{{3}^{2}}+{{4}^{2}}} \\
& =\sqrt{25} \\
& =5
\end{align}$
Hence, the length of the line segment is $5$ units. Calculate the midpoint $\left( x,y \right)$ of the line segment as follows:
$\begin{align}
& x=\frac{2+5}{2} \\
& =\frac{7}{2}.
\end{align}$
$\begin{align}
& y=\frac{-2+2}{2} \\
& =0.
\end{align}$
Hence, the midpoint of the line segment is $\left( \frac{7}{2},0 \right)$.
