The points are $P(a,-11), Q(5, b), R(2,15)$ and $S(1,1)$

Join PR and QS, intersecting at 0 .

Since,the diagonals of a parallelogram bisect each other Therefore, 0 is the midpoint of PR as well as $Q S$.

Midpoint of $P R=\left(\frac{a+2}{2}, \frac{-11+15}{2}\right)=\left(\frac{a+2}{2}, \frac{4}{2}\right)=\left(\frac{a+2}{2}, 2\right)$

Midpoint of $Q S=\left(\frac{5+1}{2}, \frac{b+1}{2}\right)=\left(\frac{6}{2}, \frac{b+1}{2}\right)=\left(3, \frac{b+1}{2}\right)$

Therefore, $\frac{a+2}{2}=3, \frac{b+1}{2}=2$

$$
\begin{aligned}
&\Rightarrow a+2=6, b+1=4 \\
&\Rightarrow a=6-2, b=4-1 \\
&\Rightarrow a=4 \text { and } b=3
\end{aligned}
$$