Which set of points are defined by the relation $x/|x|=y/|y|$?
I think the answer is a straight line bisecting the first and third quadrants through the origin ( ie the line x=y). However wolfram alpha gives a very different result. Where am I going wrong?
On
Let's have some questions:
1- Is one of $x=0$ or $y=0$ allowed to be happen?
No
2- So let $x\neq 0$and $y\neq0$. What we have if $x>0$ and $y<0$?
Indeed, $1=-1$ which is forbidden.
3- what we will be there if $x>0$ and $y>0$ or $x<0$ and $y<0$.
Indeed, we will face to the identity $1=1$.
Conclusion: All $(x,y)$ wherein $x>0,y>0$ or $x<0,y<0$ are the solutions.
What if $x > 0$ and $y > 0$? Then we have $1=1$. This means that $(x,y)$ is a point in your set provided $x$ and $y$ are positive.
If both are negative, then we find $-1=-1$.
This does not work if $x>0$ and $y<0$ or the other way around since $1\neq -1$.
Neither $x$ nor $y$ are allowed to be zero. Since the relation would be undefined.
Thus we have the set you are looking for is the union of the first and third quadrants of the plane.