Question

The diagonal of a square is $8x-15y=0$ and one vertex of the square is $(1,2)$. Then the equations to the sides of the square passing through the vertex are

• A. $22x+8y=9$, $22x-8y=52$
• B. $23x+7y=9$, $7x-23y=52$
• C. $23x-7y=9$, $7x+23y=53$
• D. $22x+8y=9$, $22x+8y=52$

Answer 1

Answer: (C)

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

REF.Image.

A] Let ABCD be square &

D(1,2)

$BD=8x-15y=0$

Slope of $BD=\frac{8}{15}$

$\angle$ made by BD with AD & CD is ${45}^{\circ }$

Let slope of DC be x.

so,

$tan{45}^{\circ }=\frac{x-\frac{8}{15}}{1+\frac{8x}{15}}$

$\Rightarrow 15+8x=15x-8$

$\Rightarrow 15+8=(15-8)x$

$\Rightarrow 7x=23$

$\therefore x=\frac{23}{7}$

$\therefore$ equation of DC is :-

$y-2=\frac{23}{7}(x-1)$

$\Rightarrow 23x-7y-9=0$

${111}^{\prime y}$ equation of AD is

$y-2=\frac{-7}{23}(x-1)$

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