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Q.
If $ (-4,\,\,5) $ is one vertex and $ 7x-y+8=0 $ is one diagonal of a square, then the equation of the second diagonal is:
Jharkhand CECEJharkhand CECE 2005
Solution:
In a square two diagonals intersect perpendicularly.
Since, equation of one diagonal of a square is $ 7x-y+8=0 $
$ \therefore $ The equation of another diagonal will be $ x+7y+\lambda =0 $.
This diagonal passes through the point $ (-4, 5) $ .
$ \therefore -4+35+\lambda =0$
$\Rightarrow \lambda =-31 $
$ \therefore $ The required diagonal is, $ x+7y=31 $