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
• B. $P$ cannot lie inside the triangle $OAB$
• C. $P$ lies inside the triangle $OAB$ only
• D. $P$ lies in the first quadrant only

Answer 1

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

Since $xy>0$, 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.