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Question

# Let O be the origin. If A(1,0),B(0,1) and P(x,y) are points such that xy>0 and x+y<1, then

A
P lies either inside the triangle OAB or in the third quadrant
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B
P cannot lie inside the triangle OAB
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C
P lies inside the triangle OAB only
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D
P lies in the first quadrant only
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Solution

## The correct option is A P lies either inside the triangle OAB or in the third quadrantSince xy>0, P lies either in the first quadrant or in the third quadrant. The inequality x+y<1 represents all points below the line x+y=1. Hence, point P lies inside the triangle OAB or lies in the third quadrant.

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