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The equations of the sides of a parallelogram are $x = 2, x = 3$ and $y = 1, y = 5$ .Equations to the pair of diagonals are

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$x + 4 y = 13, x - 4 y = 7$

$4 x + y = 7, 4 x - y = 13$

$x + 4 y = 7, x - 4 y = 13$

$4 x + y = 13, 4 x - y = 7$

answer is D.

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Detailed Solution

The vertices of the parallelogram are

$A (2, 1), B (2, 5), C (3, 5)$ and $D (3, 1)$

Equation of the diagonal $A C$ is

$y - 1 = \frac{5 - 1}{3 - 2} (x - 2) \Rightarrow 4 x - y = 7$

Equation of the diagonal $B D$ is

$y - 5 = \frac{1 - 5}{3 - 2} (x - 2) \Rightarrow 4 x + y = 13$

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