The co-ordinates of the four vertices of quadrilateral are `(-2,4),(-1,2), (1, 2) and (2, 4),` taken in order. The equation of the line through the vertex `(-1, 2)` and dividing the quadrilateral in two`equal parts is:

Options

A. x + 1 = 0
B. x + y = 1
C. x - y + 3 = 0
D. none of these

Explanation

Clearly , ABCD is a trapezium symmetric about y-axis .

Let BE be the required line such that DE = `lambda` . Then ,
Area of quadrilateral BCDE = `(1)/(2)` Area of trapezium ABCD
`implies (1)/(2) (2 + lambda) xx 2 = (1)/(2) xx (1)/(2) (2 + 4) xx 2`
`implies 2 + lambda = 3 implies lambda = 1` .
Thus , the coordinates of E are (1,4)
Hence , the equation of BE is
`y -2 = (4-2)/(1+1) (x + 1) implies x - y + 3 = 0`