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