Question

In a $△ABC$, if $A$ is $(2,-1)$ and $7x-10y+1=0$ and $3x-2y+5=0$ are equations of an altitude and an angle bisector, respectively, drawn from $B$, then equation of $BC$ is

• A. $x+y+1=0$
• B. $5x+y+17=0$
• C. $4x+9y+30=0$
• D. $x-5y-7=0$

Answer 1

Answer: (B)

$5x+y+17=0$

Altitude BD and angle bisector BE intersect at $B$. Coordinates of $B$ are $(-3,-2)$.

$m_{AB}=\frac{1}{5}$

$\Rightarrow \tan \theta =\left|\frac{\frac{3}{2}-\frac{1}{5}}{1+\frac{3}{10}}\right|=\left|\frac{\frac{3}{2}-m}{1+\frac{3m}{2}}\right|$

$\Rightarrow 1=\left|\frac{3-2m}{2+3m}\right|$

$\Rightarrow \pm 1=\frac{3-2m}{2+3m}$

$\Rightarrow m=\frac{1}{5}$ (rejected) or $-5$

Equation of $BC$ is,

$y+2=-5(x+3)$

$\Rightarrow 5x+y+17=0$