First slide

Equation of line in Straight lines

Question

One diagonal of a square is along the line 8x - l5y=0 and one of its vertex is ( l, 2). Then the equations of the sides ofthe square passing through this vertex are

Moderate

A

$23 x + 7 y = 9, 7 x + 23 y = 53$
B

$23 x - 7 y + 9 = 0, 7 x + 23 y + 53 = 0$
C

$23 x - 7 y - 9 = 0, 7 x + 23 y - 53 = 0$
D

None of these

Solution

$The slope of B D is 8 / 15 and the angle made by B D with D C$
$and B C is 45^{\circ} . So, let the slope of D C be m . Then,$
$\begin{aligned} \tan 45^{\circ} = \pm \frac{m - \frac{8}{15}}{1 + \frac{8}{15} m} \\ or (15 + 8 m) = \pm (15 m - 8) \\ or m = \frac{23}{7} and - \frac{7}{23} \end{aligned}$
Hence, the equations of DC and BC are
$\begin{aligned} y - 2 = \frac{23}{7} (x - 1) \\ or 23 x - 7 y - 9 = 0 \\ and y - 2 = - \frac{7}{23} (x - 1) \\ or 7 x + 23 y - 53 = 0 \end{aligned}$

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