CAT 2018 Question Paper Shift 2 Solved Paper

Since we want point $\mathit{A}$ to be as close to the origin as possible, let point $\mathit{A}$ lie on the $\mathit{x}$ axis and its coordinates be $\left(\mathit{a},0\right)$
The distance of A from side $\mathit{B}\mathit{C}$ (lying on the line $\mathit{x}=4$ ) is the height of the triangle
$\Rightarrow$ The height of the triangle $\mathit{A}\mathit{B}\mathit{C}=|\mathit{a}-4|$
Given the area of the triangle $=32$
$\Rightarrow \mathit{a}=12$ or -4
Required answer is the shortest distance from (0,0) i.e. 4 when $\mathit{a}=-4$.