Question

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

• A. $x+7y-31=0$
• B. $x+7y-15=0$
• C. $x+7y+8=0$
• D. $7x-y-31=0$

Answer 1

The correct option is A $x+7y-31=0$

If $(-4,5)$ is one vertex and $7x-y+8=0$ ………..$\left(1\right)$

It is one diagonal of square.

But, we know that diagonal of square are perpendicular.

So, equation of perpendicular is

$x+7y=\lambda$ ………..$\left(2\right)$

point $(-4,5)$

then,

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

$-4+35=\lambda$

$\lambda 31$

Put in equation $\left(2\right)$

$x+7y=31$

$x+7y-31=0$

Hence, this equation of second diagonal of square.