A point moves in such a way that the sum of its distance from $xy$-plane and $yz$-plane remains equal to its distance from $zx$-plane. The locus of the point is

The correct option is D. $x+z-y=0$

We know that,

Distance from $xy$-plane to the point $P(x,y,z)=|z|$

Distance from $zx$-plane to the point $P(x,y,z)=|y|$

Distance from $yz$-plane to the point $P(x,y,z)=|x|$

It is given that,

the sum of its distance from $xy$-plane and $yz$-plane remains equal to its distance from $zx$-plane

$\Rightarrow |x|+|z|=|y|$

$\Rightarrow x+z-y=0$