Question

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

• A. $x+1=0$
• B. $x+y=1$
• C. $2x-3y+8=0$
• D. $noneofthese$

Answer 1

The correct option is C $2x-3y+8=0$

This quadrilateral is isosceles trapezium.
Line from vertex $(-1,2)$ divides this trapezium into two equal parts when it also passes through $(2,4)$
Hence, the equation of required line is $2x-3y+8=0$