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Q.
Let $P$ be $(5,3)$ and a point $R$ on $y=x$ and $Q$ on the $x$-axis be such that $P Q+Q R+R P$ is minimum. Then the coordinates of $Q$ are
Straight Lines
Solution:
$P^{\prime}$ and $P^{\prime \prime}$ are the images of $P$ w.r.t. $y=x$ and $y=0$, respectively.
Therefore, $P^{\prime} \equiv(3,5)$.
The equation of $P^{\prime} P^{\prime \prime}$ is
$ y+3=\frac{5+3}{3-5}(x-5) $
$\therefore x=5+3\left(-\frac{1}{4}\right)=\frac{17}{4} $
$\therefore Q \equiv\left(\frac{17}{4}, 0\right)$
