Question

The point $(-4,5)$ 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

Answer: (B)

$x+7y=31$

We know that the diagonals of a square intersects each other at right angle. Both are perpendicular.

We know that, equation of perpendicular line to $7x-y+8=0$ is $x+7y=\lambda$ ……… (1)

Which is passes through $(-4,5)$

Then,

$-4+7\left(5\right)=\lambda$

$\lambda =31$

So, by equation (1), $x+7y=31$ (another diagonal equation )

option $B$ is correct