Question

If the equation of the hypotenuse of a right-angled isosceles triangle is $3x+4y=4$ and its opposite vertex is $\left(2,2\right)$ , then the equations of the perpendicular and the base are respectively

• A. $7x+y=16\&x-7y+12=0$
• B. $7x-y=12\&x+7y=16$
• C. $5x+y=12\&x-5y+8=0$
• D. $x+5y=12\&5x-y=8$

Answer 1

Answer: (A)

Let, the slope of the required line is $m$ , then
$\frac{m-\left(-\frac{3}{4}\right)}{1+m\left(-\frac{3}{4}\right)}=\pm tan{\left(45\right)}^o$
$4m+3=\pm \left(4-3m\right)$
$\Rightarrow m=-7,\frac{1}{7}$
$\Rightarrow$ equation of the lines are $\frac{y-2}{x-2}=-7$ & $\frac{y-2}{x-2}=\frac{1}{7}$
$\Rightarrow 7x+y=16\&x-7y+12=0$