Question

The vertex 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 _______________

Answer 1

$AB=\sqrt{(-1-5{)}^2+(-7-1{)}^2}$

$=10$

$BC=\sqrt{(1-(5){)}^2+(4-1{)}^2}$

$=5$

$BD$ divides $AC$ in ratio $10:5$

$2:1$

$D(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Equation of $BD$ is

$y-1=\frac{1-\frac{1}{3}}{5-\frac{1}{3}}(x-5)$

Simplifying

$x+2=7y$.