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Area of the parallelogram formed by the ...

Area of the parallelogram formed by the lines y = mx, y = mx + 1,y = nx and y =nx+1 equals to

A

`(|m+n|)/((m-n)^(2))`

B

`(2)/(|m+n|)`

C

`(1)/(|m+n|)`

D

`(1)/(|m-n|)`

Text Solution

Verified by Experts

Let lines `OB : y =mx`
`CA : y=mx+1`
`BA : y=nx+1`
and `OC : y=nx`
The point of intersection `B` of `OB` and `AB` has `x` coordinate `(1)/(m-n)`.

Now, area of a parallelogram `OBAC`
`=2xx"area Of" DeltaOBA`
`=2xx(1)/(2)xxOAxxOB=2xx(1)/(2)xx(1)/(m-n)`
`=(1)/(m-n)=(1)/(|m-n|)`
depending upon whether `m gt n` or `m lt n`.
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