Question

Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is $3x+4y=4$ and the opposite vertex of the hypotenuse is $(2,2)$, will be ?

• A. $x-7y+12=0$
• B. $7x+y-12=0$
• C. $x-7y+16=0$
• D. $7x+y+16=0$

Answer 1

The correct option is A $x-7y+12=0$

The equation of hypotenuse is $3x+4y=4$

Hence the slope of the line is $-3/4$

$\because$ It is isosceles right angled triangle,

angles are $45°,45°$ & $90°$

$\tan 45°=\left|\frac{m-(-3/4)}{1+m(-3/4)}\right|$

$\tan 45°=1$

$1-\frac{3m}{4}=\pm (m+\frac{3}{4})$

If $1-\frac{3m}{4}=m+\frac{3}{4}$

$\frac{7m}{4}=\frac{1}{4}$

$m=\frac{1}{7}$

The co ordinates of $B=(2,2)$

The equation of line AB is

$(y-2)=1/7(x-2)$

$x-7y+12=0$