If four vertices of a parallelogram taken in order are $\left(-3,-1\right),\left(a,b\right),\left(3,3\right)$  and $\left(4,3\right)$ . What will be the ratio of $a\text{and}b$ is

So coordinates of the mid-point of $AC=$  coordinates of the mid-point of $BD$ [$\therefore$ In parallelogram, diagonals bisect each other]

$\Rightarrow \left(\frac{-3+3}{2},\frac{-1+3}{2}\right)=\left(\frac{a+4}{2},\frac{b+3}{2}\right)$

$\Rightarrow \left(0,1\right)=\left(\frac{a+4}{2},\frac{b+3}{2}\right)$

$\Rightarrow \frac{a+4}{2}=0\text{and}\frac{b+3}{2}=1$

$\Rightarrow a=-4,b=-1$

Now $\frac{a}{b}=\frac{-4}{-1}=\frac{4}{1}$

$\Rightarrow a:b=4:1$