#### Answer

$(\frac{1}{20},-\frac{3}{16})$

#### Work Step by Step

Let $P=(x_{1},y_{1})=(0,-\frac{3}{8})$ and $Q=(x_{2},y_{2})=(\frac{1}{10},0)$
The midpoint formula is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$.
Substituting the values:
Midpoint=$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
Midpoint=$(\frac{0+\frac{1}{10}}{2},\frac{-\frac{3}{8}+0}{2})$
Midpoint=$(\frac{\frac{1}{10}}{2},\frac{-\frac{3}{8}}{2})$
Midpoint=$(\frac{1}{10}\times\frac{1}{2},-\frac{3}{8}\times\frac{1}{2})$
Midpoint=$(\frac{1}{20},-\frac{3}{16})$
Therefore, the coordinates of the midpoint are $(\frac{1}{20},-\frac{3}{16})$.