Question

If the coordinates of the four vertices of a quadrilateral are $(-2,4),(-1,2),(1,2)$ and $(2,4)$ taken in order, then the equation of line passing through the vertex $(-1,2)$ and dividing the quadrilateral in two equal areas is

• A. $x+1=0$
• B. $x+y-1=0$
• C. $x-y+3=0$
• D. $x-y-3=0$

Answer 1

The correct option is C $x-y+3=0$

Clearly, $ABCD$ is a trapezium symmetric about $y$ -axis.
Let $BE$ be the required line such that $DE=\lambda$.


Now,
Area of triangle $ABE$
$=\frac{1}{2}$ Area of trapezium $ABCD$
$\Rightarrow \frac{1}{2}\times h\times AE=\frac{1}{2}\times \frac{1}{2}(2+4)\times h\Rightarrow AE=3\Rightarrow 4-\lambda =3\Rightarrow \lambda =1$
Thus, the coordinates of $E$ are $(1,4)$
Therefore, the equation of $BE$ is
$y-2=\frac{4-2}{1+1}(x+1)\Rightarrow x-y+3=0$