Locus question?

Question

Just wondering how you would solve this:

"Find the locus of a point $P(x,y)$ which moves such that its distance from the $x$-axis is always one more unit than its distance from the $y$-axis."

Thanks

Answer 1

The perpendicular distance of point $(x,y)$ from the $x$ axis is $|y|$ and the distance from the $y$ axis is $|x|$.

So, $|y|=|x|+1$.

For $y\geq0$, the graph is $y=|x|+1$ and for $y<0$, the graph is given by $y=-|x|-1$.