# Locus problem defined through distance

Question

If the distance of any point $$(x,y)$$ from the origin is defined as $$d(x,y)=max(|x|,|y|)$$, $$d(x,y)=a$$, non zero constant,then the locus is___.

My attempt

In question the equation for d is the max absolute value of the coordinate (whether x or y). So if we take square whose center is the origin and of side length 2a then it satisfies the given condition as whatever point we choose on square it will have x or y coordinate to be $$a$$.

Is this right? Because answer given by the test solution states it to be straight line(Multi choice questions test).

• Yep, you're right. – Frpzzd Oct 1 '18 at 19:25