Question

Let $O$ be the origin, and let $A(1,0),B(0,1)$ be two points. If $P(x,y)$ is a point such that $xy>0$ and $x+y<1,$ then

• A. $P$ lies either in side $△OAB$ or in third quadrant
• B. $P$ cannot be inside $△OAB$
• C. $P$ lies inside the $△OAB$
• D. none of these

Answer 1

The correct option is A $P$ lies either in side $△OAB$ or in third quadrant

Given two points

$A(1,0),B(0,1)$

Since $xy>0$

P lies either in first quadrant or third quadrant

and $x+y<1$ it represent all points below the line $x+y=1$

Hence P lies inside the $△OAB$ or in third quadrant