Question

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

• A. $P$ lies either inside the $△OAB$ or in the third quadrant
• B. $P$ can not lie inside the $△OAB$
• C. $P$ lies inside the $△OAB$
• D. $P$ lies in the first quadrant only

Answer 1

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

Since $xy>0,P$ either lies in the first quadrant or in the third quadrant. The inequality $x+y<1$ represents all points below the line $x+y=1.$ So that $xy>0$ and $x+y<1$ imply that either $P$ lies inside the triangle$OAB$ or in the third quadrant