Question

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

• A. $7x-y=23$
• B. $x+7y=31$
• C. $x-7y=31$
• D. None of these

Answer 1

The correct option is B $x+7y=31$

The equation of diagonal is $7x-y+8=0$

The diagonal is perpendicular

So the equation of diagonal is $x+7y+k=0$

This passes through $(-4,5)$

$⟹(-4)+7\left(5\right)+k=0$

$⟹-4+35+k=0$

$⟹k=-31$

The other diagonal is given as $x+7y-31=0$

$⟹x+7y=31$