Question

A delivery man drives his bike from the point $A(5,-2)$ and collects the order from the store $C$, which lies on $y$ - axis. He then delivers the order to $B(3,2).$
If the distance covered by the delivery man is minimum, then the co-ordinates of $C$ is

• A. $(0,\frac{1}{4})$
• B. $(0,\frac{1}{6})$
• C. $(0,\frac{1}{2})$
• D. $(0,1)$

Answer 1

The correct option is C $(0,\frac{1}{2})$

$AC+CB$ needs to be minimum


Let's take the image of $B(3,2)$ about $y$-axis
$\Rightarrow CB=C{B}^{\prime }$, where $B^{\prime }(-3,2)$ is the image of $B$

$\Rightarrow (AC+CB{)}_{\text{min}}=(AC+C{B}^{\prime }{)}_{\text{min}}$

$\text{Slope of}AC=\text{Slope of}A{B}^{\prime }\frac{y+2}{0-5}=\frac{-2-2}{5+3}y=\frac{1}{2}\Rightarrow C(0,\frac{1}{2})$