In a triangle P Q R , the co-ordinates of the points P and Q are - 2 , 4 and 4 , - 2 respectively. If the…

Perpendicular bisector of $PR$ is $2x-y+2=0$ 

Midpoint of $PQ$ is $M\left(1,1\right)$

Equation of perpendicular bisector of $PQ$ is $y=x$.

Point of intersection of equations $PR$ and $PQ$ is circumcentre.

So, circumcentre is $\left(-2,-2\right)$