A (-1, 1), B (5, 3) are opposite vertices of a square. The equation of the other diagonal ( not passing through A, B) of the square is

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$2 x - 3 y + 4 = 0$

$2 x - y + 3 = 0$

$y + 3 x - 8 = 0$

$x + 2 y - 1 = 0$

answer is C.

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Detailed Solution

Let A (-1 , 1) B (5, 3)

P = Mid point of AB

$\begin{array}{l} = (\frac{5 - 1}{2}, \frac{3 + 1}{2}) \\ = (2, 2) = (x_{1}, y_{1}) \end{array}$

$\begin{array}{l} S l o p e o f \bar{A B} = \frac{3 - 1}{5 + 1} = \frac{2}{6} = \frac{1}{3} \\ \bar{A B} ⊥ \bar{C D} \Rightarrow m = S l o p e o f \bar{C D} = \frac{- 1}{S l o p e o f \bar{A B}} = - 3 \end{array}$

$\begin{array}{l} E q u a t i o n o f \bar{C D} i s y - y_{1} = m (x - x_{1}) \\ \Rightarrow y - 2 = - 3 (x - 2) \\ \Rightarrow y - 2 = - 3 x + 6 \\ \Rightarrow 3 x + y - 8 = 0 \end{array}$