First slide

Equation of line in Straight lines

Question

The equations to a pair of opposite sides o fa parallelogram $are x^{2} - 5 x + 6 = 0 {and y}^{2} - 6 y + 5 = 0 . The equations to$ $its diagonals are$

Moderate

A

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

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

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

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

Solution

The sides of parallelogram are
$x = 2, x = 3, y = 1, y = 5$
The equation of diagonal AC is

$\begin{aligned} \frac{y - 1}{5 - 1} = \frac{x - 2}{3 - 2} \\ or y = 4 x - 7 \end{aligned}$
and the equation of diagonal BD is
$\begin{aligned} \frac{x - 2}{3 - 2} = \frac{y - 5}{1 - 5} \\ or 4 x + y = 13 \end{aligned}$

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