Question

If points $(x,0)$, $(0,y)$ and $(1,1)$ are collinear then the relation is-

• A. $x+y=1$
• B. $x+y=xy$
• C. $x+y+1=0$
• D. $x+y+xy=0$

Answer 1

The correct option is B $x+y=xy$

Area of a triangle with vertices $(x_1,y_1)$ ; $(x_2,y_2)$ and $(x_3,y_3)$ is $\left|\frac{x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}{2}\right|$
Since the given points are collinear, they do not form a triangle, which means area of the triangle is zero.
Hence, substituting the points $(x_1,y_1)=(x,0)$ ; $(x_2,y_2)=(0,y)$ and $(x_3,y_3)=(1,1)$ in the area formula, we get
$\left|\frac{x(y-1)+0(1-0)+1(0-y)}{2}\right|=0$
$=>xy-x-y=0$
$=>x+y=xy$
Hence, option 'B' is correct.