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. $x+3y=21$
• B. $2x-3y=7$
• C. $x+7y=31$
• D. $2x+3y=21$

Answer 1

Answer: (C)

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, $x+7y=31$