Question

Let $B_1\equiv 3x+4y-7=0$ & $B_2\equiv 4x-3x-14=0$ are the angle bisectors of the angle between the lines $L_1=0$ & $L_2=0,$ in which $L_1$ is passes through the point $(1,2)$, then

• A. $B_1$ is acute angle bisector
• B. $B_2$ is acute angle bisector
• C. $B_1$ & $B_2$ both are right angle bisector
• D. Data is insufficient

Answer 1

Answer: (A)

$B_1$ is acute angle bisector

Line $L_1$ passes through point $(1,2)$

Let the perpendicular distance from Point $(1,2)$ of given bisector $B_1:3x+4y-7=0$ is u then

$u=\left|\frac{3+8-7}{\sqrt{3^2+4^2}}\right|$

$u=\left|\frac{4}{\sqrt{25}}\right|\Rightarrow u=\frac{4}{5}$

Let the perpendicular distance from Point $(1,2)$ of given bisector $B_2:4x-3y-14=0$ is v then

$v=\left|\frac{4-6-20}{\sqrt{3^2+4^2}}\right|$

$v=\left|\frac{-16}{\sqrt{25}}\right|\Rightarrow v=\frac{16}{5}$

Here $u<v$ then $B_1$ is the acute angle bisector