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  4. The point ( - 4, 5) is the vertex of a square and one of its diagonals is 7 x -y + 8 = 0. The equation of the other diagonal is

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Q. The point $( - 4, 5)$ is the vertex of a square and one of its diagonals is $7 x -y + 8 = 0$. The equation of the other diagonal is

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Solution:

As we know that diagonals of a square are perpendicular to each other

Let the equation of other diagonal is

$x + 7y = k$

Also, passes through $( - 4, 5)$

$\therefore - 4 + 35 =k $

$\Rightarrow k=31$

$\therefore $ Required equation is $x + 7y - 31 = 0$