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Which of the following is / are true ? ...

Which of the following is / are true ?
(a) If |x+y|=|x|+|y| then points (x,y) lie in 1st or 3rd quadrant or any of the x-axis or y axis
(b) If `|x+y| lt |x|+|y|` then points (x,y) lie in 2nd or 4th quadrant.
(c ) If |x-y|=|x|+|y| then points (x,y) lie in 2nd or 4th quadrant.

Text Solution

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The correct Answer is:
All
|x+y|=|x|+|y|
`rArr` x and y have same sign or at least one of x and y is zero .
`rArr` (x,y) lies in 1st or 3rd quadreant or any of the x-axis or y-axis
|x+Y| lt |x| +|y|
`rArr ` x and -y have opposite sign
`rArr ` x and y have opposite sign
`rArr` (x,y) lies in 2nd or 4th quadreant at least on of x and y is zero .
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