If the three vertices of a parallelogram are $(a+b,a-b),(2a+b,2a-b),(a-b,a+b)$ then the fourth vertex is

Mid point of $AC=$Mid point of $BD$

$\left(\frac{a+b+a-b}{2},\frac{a-b+a+b}{2}\right)=\left(\frac{2a+b+x}{2},\frac{2a-b+y}{2}\right)$

$(a,a)=\left(\frac{2a+b+x}{2},\frac{2a-b+y}{2}\right)$

$2a=2a+b+x,2a=2a-b+y$

$x=-b,y=b$

$\text{Fourth\hspace{0.17em}vertex}=(-b,b)$