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One side of a rectangle lies along the l...

One side of a rectangle lies along the line 4x+7y+5=0. Two of its vertices are (-3,1) and (1,1). Find the equations of the other three sides.

Text Solution

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Since, the side `AB` is perpendicular to `AD`.

`:.` Its equation is of the form `7x-4y+lambda=0`
Since, it passes through `(-3,1)`
`:. 7(-3)-4(1)+lambda=0`
`implieslambda=25`
`:.` Equation of `AB` is
`7x-4y+25=0`
Now, `BC` is parallel to `AD`. Therefore, its equation is
`4x+7y+lambda=0`
Since, it passes through `(1,1)`.
`:. 4(1)+7(1)+lambda=0`
`implieslambda=-11`
`:.` Equation of `BC` is `4x+7y-11=0`
Now, equation of `DC` is `7x-4y+lambda=0`
`implies7(1)-4(1)+lambda=0`
`implieslambda=-3`
`:. 7x-4y-3=0`
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