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

The Correct Option is B

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)