Question

The angular points of a triangle are $A(-1,-7),B(5,1)$ and $C(1,4)$. The equation of the bisector of the angle $\angle ABC$ is

• A. $x=7y+2$
• B. $7y=x+2$
• C. $y=7x+2$
• D. $7x=y+2$

Answer 1

The correct option is B $7y=x+2$

$AB=\sqrt{36+64}=10,BC=\sqrt{16+9}=5$
$D(\frac{-1+2}{3},\frac{-7+8}{3})=D(\frac{1}{3},\frac{1}{3})$
$\therefore$ Equation of $BD$ is $y-1=\frac{1-\frac{1}{3}}{5-\frac{1}{3}}(-5)$
$y-1=\frac{2}{14}(x-5)$
$7y-7=x-5$
$\therefore$ $x-7y+2=0$
$\Rightarrow$ $x+2=7y$