Question

Find the equation of the altitude AD of the triangle whose vertices are $(7,-1)$, $(-2,8)$ and $(1,2)$.

• A. $3x-2y-9=0$
• B. $x-2y-9=0$
• C. $x-y-9=0$
• D. $x-2y-8=0$

Answer 1

The correct option is B

$x-2y-9=0$

Slope of $\left(BC\right)=\frac{2-8}{1+2}=\frac{-6}{3}=-2$
$\therefore$ slope of $\left(AD\right)=\frac{1}{2}$ [as the lines are perpendicular]
Equation of AD is $y-y_1=m(x-x_1)$ [Point Slope form]
$\Rightarrow$ $y+1=\frac{1}{2}(x-7)$
$\Rightarrow$ $2y+2=x-7$ or $x-2y-9=0$