#### Answer

$(\frac{1}{4},-\frac{2}{7})$

#### Work Step by Step

Let $P=(x_{1},y_{1})=(\frac{3}{4},-\frac{1}{7})$ and $Q=(x_{2},y_{2})=(-\frac{1}{4},-\frac{3}{7})$
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=$(\frac{\frac{3}{4}-\frac{1}{4}}{2},\frac{-\frac{1}{7}-\frac{3}{7}}{2})$
Midpoint=$(\frac{\frac{3-1}{4}}{2},\frac{\frac{-1-3}{7}}{2})$
Midpoint=$(\frac{\frac{2}{4}}{2},\frac{\frac{-4}{7}}{2})$
Midpoint=$(\frac{\frac{1}{2}}{2},\frac{\frac{-4}{7}}{2})$
Midpoint=$(\frac{1}{2}\times\frac{1}{2},-\frac{4}{7}\times\frac{1}{2})$
Midpoint=$(\frac{1}{4},-\frac{4}{14})$
Midpoint=$(\frac{1}{4},-\frac{2}{7})$
Therefore, the coordinates of the midpoint are $(\frac{1}{4},-\frac{2}{7})$.