Question

In a triangle $PQR,$ the co-ordinates of the points $P$ and $Q$ are $(-2,4)$ and $(4,-2)$ respectively. If the equation of the perpendicular bisector of $PR$ is $2x-y+2=0,$ then the centre of the circumcircle of the $\Delta PQR$ is:

• A. $(-2,-2)$
• B. $(0,2)$
• C. $(-1,0)$
• D. $(1,4)$

Answer 1

The correct option is A $(-2,-2)$


Perpendicular bisector of $PR$ is
$2x-y+2=0\cdots \left(1\right)$
Mid-points of $PQ$ is $M\equiv (1,1)$
Equation of perpendicular bisector of $PQ$ is
$y-1=-\left(\frac{4+2}{-2-4}\right)(x-1)\Rightarrow x=y\cdots \left(2\right)$

Therefore, circumcentre is point of intersection of the two perpendicular bisectors i.e., $(-2,-2)$