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The area (in sq unit) of the triangle fo...

The area (in sq unit) of the triangle formed by `x+y+1=0` and the pair of straight lines `x^2-3xy+2y^2=0` is

A

`(7)/(12)`

B

`(5)/(12)`

C

`(1)/(12)`

D

`(1)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `x^2-2xy-xy+2y^2=0`
`rArr (x-2y)(x-y)=0`
`rArr x=2y` .....(i)
and `x=y` ......(ii)
Also , `x+y=1=0` .......(iii)
On solving Eqs. (i) , (ii) and (iii) , we get
`A(-(2)/(3),-(1)/(3)),B(-(1)/(2),-(1)/(2)), C(0,0)`
`therefore` Area of `Delta ABC=(1)/(2) |{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}|=(1)/(2)|{:(-(2)/(3),-(1)/(3),1),(-(1)/(2),-(1)/(2),1),(0,0,1):}|=(1)/(2)[(1)/(2)-(1)/(6)]=(1)/(2)[(1)/(6)]=(1)/(12)"sq unit"`
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