# plotting the following set of points in the XY plane

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,

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What you have works. You can check this by noting that if x or y<0, then -x or -y is positive, and thus you can use -x or -y for |x| or |y| in the original equation. If x or y>0, then use x or y in the original equation. What's your question exactly? –  Doug Spoonwood Jun 10 '12 at 10:20

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.