Search any question & find its solution
Question:
Answered & Verified by Expert
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 $\Delta P Q Q^{\prime}$ is
Options:
Solution:
1851 Upvotes
Verified Answer
The correct answer is:
(0,0)
The coordinates of $Q$ and $Q^{\prime}$ will be (6,3)
and $(-3,-6),$ respectively. Now, slope of $P Q=\frac{6-3}{3-6}=-1$ and Slope of $Q Q^{\prime}=\frac{-6-3}{-3-6}=1$
$\therefore$ Slope of $P Q \times$ Slope of $Q Q^{\prime}=-1 \times 1=-1$
$\therefore \Delta P Q Q^{\prime}$ is right angled triangle at $Q .$
$\therefore$ Circumcentre will be the mid-point of hypotenuse $P Q^{\prime}=\left(\frac{-3+3}{2}, \frac{-6+6}{2}\right)$
$$
=(0,0)
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.