Question

If the distance of any point $(x,y)$ from the origin is defined as $d(x,y)=max\{\left|x\right|,\left|y\right|\}$ then the locus of the point $(x,y)$ where $d(x,y)=1$, is

• A. A square
• B. A circle
• C. A triangle
• D. None the above

Answer 1

The correct option is A A square

We have
$d(x,y)=1$
$\Rightarrow max\{\left|x\right|,\left|y\right|\}=1$
$\Rightarrow \left|x\right|\le 1$
$\left|y\right|\le 1$
$\Rightarrow -1\le x\le 1$ and $-1\le y\le 1$
$\therefore$ Locus of $(x,y)$ is the squaring having its vertices at $(1,1),(-1,1),(-1,-1)$ and $(1,-1)$