Question

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

• A. $x-7y+2=0$
• B. $3x-3y-7=0$
• C. $3x-7y-8=0$
• D. $3x+7y+2=0$

Answer 1

The correct option is A $x-7y+2=0$

The vertices of a triangle are $A(-1,-7),B(5,1),C(1,4)$
Here $AB=10,BC=5$
The internal bisector of $\angle ABC$ will divide the opposite side $AC$ in the ratio $5:1O$
$\therefore$ Point $D$ have the co-ordinates (using section formula)
as $(\frac{1}{3},\frac{1}{3})$
$\therefore$ Equation of $BD$ is $x-7y+2=0$
Hence the choice (a) is correct answer.