Mathematics - Application of Derivative Question with Solution | TestHub

$P$ and $Q$ lie on the same side of $2x+y=7(2(3)+(-3)=3<7$ and $0+2=2<7$ ), so reflect $P$ in the line: the image is $P^{\prime }=\left(\frac{31}{5},-\frac{7}{5}\right)$. Then the least value of $PR+RQ$ is $P^{\prime }Q=\sqrt{{\left(\frac{31}{5}\right)}^2+{\left(-\frac{7}{5}-2\right)}^2}=$ $\sqrt{\frac{961+289}{25}}=\sqrt{50}=5\sqrt{2}$.