Question

One diagonal of a square is along the line $8 x - 15 y = 0$ and one of its vertex is (1, 2). Then the equation of the sides of the square passing through this vertex, are.

• 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

Answer 1

Answer: (C)

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

Answer 2

Slope of $B D$ is $\frac { 8 } { 15 }$ and angle made by $B D$ with AD and DC is $45 ^ { \circ }$. So let slope of DC be m, then $\tan 45 ^ { \circ } = \pm \frac { m - \frac { 8 } { 15 } } { 1 + \frac { 8 } { 15 } m }$

$\Rightarrow ( 15 + 8 m ) = \pm ( 15 m - 8 )$

⇒ $m = \frac { 23 } { 7 }$and $- \frac { 7 } { 23 }$

Hence the equations of DC and AD are

$y - 2 = \frac { 23 } { 7 } ( x - 1 )$ $\Rightarrow 23 x - 7 y - 9 = 0$and $y - 2 = - \frac { 7 } { 23 } ( x - 1 )$

$\Rightarrow 7 x + 23 y - 53 = 0$.