#### Answer

$\left( -\dfrac{27}{80},\dfrac{1}{24} \right)$

#### Work Step by Step

Using $\left( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)$ or the Midpoint Formula, the midpoint of the segment joining $\left(
-\dfrac{4}{5},-\dfrac{2}{3}
\right) \text{ and } \left(
\dfrac{1}{8},\dfrac{3}{4}
\right),$ is
\begin{array}{l}\require{cancel}
\left( \dfrac{-\dfrac{4}{5}+\dfrac{1}{8}}{2},\dfrac{-\dfrac{2}{3}+\dfrac{3}{4}}{2} \right)
\\\\=
\left( \dfrac{-\dfrac{27}{40}}{2},\dfrac{\dfrac{1}{12}}{2} \right)
\\\\=
\left( -\dfrac{27}{80},\dfrac{1}{24} \right)
.\end{array}