Question

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

• A. a circle
• B. a square
• C. a triangle
• D. parallelogram but not square.

Answer 1

The correct option is B a square

$d(x,y)=max|x|,|y|$

When $|x|>|y|,d(x,y)=|x|=1$
$\Rightarrow x=\pm 1$ which represent AB and CD segment.
When $|x|<|y|,d(x,y)=|y|=1$
$\Rightarrow y=\pm 1$ which represent AD and BC segment.
$\therefore$ Locus is a square ABCD.