Question

Let $P$ be $(5,3)$ and a point $R$ on $y=x$ and $Q$ on the $x$-axis be such that $PQ+QR+RP$ is minimum. Then the coordinates of $Q$ are

• A. $(17/4,0)$
• B. $(17,0)$
• C. $(17/2,0)$
• D. none of these

Answer 1

Answer: (A)

$P^{\prime }$ 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
$y+3=\frac{5+3}{3-5}(x-5)$
$\therefore x=5+3\left(-\frac{1}{4}\right)=\frac{17}{4}$
$\therefore Q\equiv \left(\frac{17}{4},0\right)$