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 = 0
• B. x + 7y = 31
• C. x – 7y = 31
• D. None of these

Answer 1

The correct option is B x + 7y = 31

Diagonals of a square bisect each other at right angles. Thus the diagonal BD is perpendicular to the
diagonal AC.

Let the equation of BD be
x + 7y + k = 0
The line (1) passes through the point B(–4, 5)
$\therefore –4+35+k=0\Rightarrow k=–31$
$therefore$ The equation of diagonal BD is x + 7y – 31 = 0