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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
$x + 1 = 0$
$x + y = 1$
$2 x - 3 y + 8 = 0$
$n o n e o f t h e s e$

A

x + 1 = 0

B

n o n e o f t h e s e

C

x + y = 1

D

2 x - 3 y + 8 = 0

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Solution

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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 $2 x - 3 y + 8 = 0$

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