Question

If the two sides AB and AC of a triangle are along $4x-3y-17 = 0$ and $3x+4y-19= 0$, then the equation of the bisector of the angle between AB and AC is ?

• A. $x + 7y+2=0$
• B. $7x-y- 36 = 0$
• C. $7x-y+ 36 = 0$
• D. $x = y$
• E. $x-7y+2 = 0$

Answer 1

Answer: (B)

$7x-y- 36 = 0$

Answer 2

Given that

The two lines of a triangle ABC in which the line AB and AC passes through the $4x-3y-17 = 0$ and $3x+4y-19= 0$

Then according to the question the Equation of Bisector of the angle can be found as follows

$\dfrac{4x-3y-17}{√(4^{2}+(-3)^{2})} =± \dfrac{3x+4y-19}{√(3^{2}+4^{2})}$

⇒$4x-3y-17= ±(3x+4y-19)$

taking Positive , the equation of bisector will be

$x-7y-2=0$

similarly taking the negative sign , the equation will be

$7x-y-36=0$

and as per the given option the right answer option $7x-y-36=0$.. (Ans)