Answer
It is located in the second quadrant or in the fourth quadrant.
Work Step by Step
First quadrant: $x\gt0$ and $y\gt0$
Second quadrant: $x\lt0$ and $y\gt0$
Third quadrant: $x\lt0$ and $y\lt0$
Fourth quadrant: $x\gt0$ and $y\lt0$
We have a point $(x,y)$ such that:
$x+y=0,~~x\ne0,~~y\ne0$
$x=-y$
That is:
- if $y\gt0$, then $x\lt0$ -> Second quadrant
- if $y\lt0$, then $x\gt0$ -> Fourth quadrant
