plotting the following set of points in the XY plane

Question

Represent the following set of points in the XY plane :

$$\{ ( x , y ) \; | \; |x| + |y| = 1 \}$$

What i got:

1) if $x > 0, y > 0 : x = 1 - y$

2) if $x > 0, y < 0 : x = 1 + y$

3) if $x < 0, y > 0 : x = y - 1$

4) if $x < 0, y < 0 : x = -y -1$

Any help to solve this question would be greatly appreciated.

Thank you,

Answer 1

Take each case without the absolute value:$$\,\,\,y=1-x$$$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;y=1-(-x)=1+x$$$$-y=1-x$$$$-y=1+x$$so you can see we get four straight lines intersecting each with other two.

Well, now just draw these lines and get your nice... rhomboid (you could know this even before drawing anything from the above equations).