In a PQR, the coordinates of the points P and Q are (-2,4) and (4,-2), respectively.

Question

In a $	riangle PQR$, the coordinates 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 $	riangle PQR$ is:

Accepted Answer

Mid point of $$PQ \equiv \left( {{{ - 2 + 4} \over 2},{{4 - 2} \over 2}} \right) \equiv (1,1)$$

Slope of $$PQ = {{4 + 2} \over { - 2 - 4}} =  - 1$$

Slope of perpendicular bisector of PQ = 1

Equation of perpendicular bisector of PQ

$y - 1 = 1(x - 1)$

$$ \Rightarrow y = x$$

Solving with perpendicular bisector of PR,

2x - y + 2 = 0

Circumcentre is (-2, -2)

Solutions · 1