Straight LineHardBloom L3
Question
A man starts from the point $P( - 3,4)$ and reaches point $Q(0,1)$ touching $x$ axis at $R$ such that $PR + RQ$ is minimum, then the point $R$ is :
Options
A.$(3/5,0)$
B.$( - 3/5,0)$
C.$( - 2/5,0)$
D.$( - 2,0)$
Solution
Sol. [Key Concept: Minimise $PR + RQ$ with $R$ on the $x$-axis by reflecting $Q$ in the axis; the minimum path is a straight line.]
$$(PR + RQ)_{\text{min}\text{~}} = \left( PR + RQ^{'} \right)_{\text{min}\text{~}} = PQ^{'}$$
$$\begin{matrix} & \ \Rightarrow \frac{0 - 4}{\lambda + 3} = \frac{4 + 1}{- 3 - 0} \\ & \ \Rightarrow \lambda = - \frac{3}{5} \\ & \ \Rightarrow R \equiv \left( - \frac{3}{5},0 \right) \end{matrix}$$
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