Question

The point $P(3,6)$ is first reflected on the line $y=x$ and then the image point $Q$ is again reflected on the line $y=-x$ to get the image point $Q^{\prime }.$ Then the circumcentre of the $△PQ{Q}^{\prime }$ is

• A. $(6,3)$
• B. $(6,3)$
• C. $(3,-6)$
• D. $(0,0)$

Answer 1

The correct option is D $(0,0)$

The point $Q$ is the reflector of $P$ and $Q^{\prime }$ is the reflector of $Q$.


In $△PQ{Q}^{\prime }$ line $y=x$ is perpendicular bisector of $PQ$ and line $y=-x$ is perpendicular bisector of $Q{Q}^{\prime }$. Both of these perpendicular bisectors of triangle are intersecting at point $O(0,0)$.
The point where two perpendicular bisectors of a triangle intersect is known as circumcenter.
Hence, the circumcenter is $O(0,0)$.