Let $P$, $Q$, $R$ and $S$ be the points on the plane with position vectors $-2\hat{i}-\hat{j}$, $4\hat{i}$, $3\hat{i}+3\hat{j}$ and $-3\hat{i}+2\hat{j}$ respectively. The quadrilateral $PQRS$ must be a

$P(-2,-1),\quad Q(4,0),\quad R(3,3),\quad S(-3,2)$

$\text{Check: sides, their lengths, and angles (dot products)}$

$\vec{PQ}=(6,1),\qquad \vec{QR}=(-1,3)$

$\vec{RS}=(-6,-1),\qquad \vec{SP}=(1,-3)$

$\vec{PQ}=-\vec{RS} \Rightarrow PQ\parallel RS,\quad PQ=RS$

$\vec{QR}=-\vec{SP} \Rightarrow QR\parallel SP,\quad QR=SP$

⇒ PQRS is a parallelogram

$|\vec{PQ}|=\sqrt{6^{2}+1^{2}}=\sqrt{37}$

$|\vec{QR}|=\sqrt{(-1)^{2}+3^{2}}=\sqrt{10}$

$\sqrt{37}\neq\sqrt{10} \Rightarrow \text{not a rhombus}$

$\vec{PQ}\cdot\vec{QR}=6(-1)+1(3)=-3\neq0$

$\Rightarrow \text{no right angle} \Rightarrow \text{not a rectangle, nor a square}$

$\Rightarrow \text{parallelogram, neither rhombus nor rectangle} \Rightarrow (1)$