• Draw perpendicular bisectors of $MN$ and $NP$.
• Construct a parallelogram using the perpendicular bisectors.

We start by connecting $M$,$N$ and $N$,$P$. Let the perpendicular bisectors of $MN$ and $NP$ intersect at $Q$. $F$,$E$ are the midpoints of $MN$ and $NP$ respectively.

Let $Q'$ be the reflection of $Q$ across $N$.

Construct parallelogram $Q'BQC$ such that $B\in QF$ and $C\in QE$.

Let $A$ and $D$ be the reflections of $B$ and $C$ across $M$ and $P$.

$\square ABCD$ is the quadrilateral Saad had drawn.