question_answer

The vertices of a triangle are A (3, 7), B (3, 4) and C (5, 4). The equation of the bisector of the angle ABC is

A)  \[y=x+1\]          

B)  \[y=x-1\]

C)  \[y=3x-5\]      

D)         \[y=x\]

E)  \[y=-x\]

Correct Answer: A

Solution :

Equation of line AB is \[y-7=\frac{4-7}{3-3}(x-3)\] \[\Rightarrow \]               \[(x-3)=0\]                                        ...(i) and equation of line BC is \[y-4=\frac{4-4}{5-3}(x-3)\]         \[\Rightarrow \]               \[y-4=0\]                 \[\therefore \]Equation of the bisector of angle ABC is \[\frac{x-3}{\sqrt{{{1}^{2}}}}=\pm \left( \frac{y-4}{\sqrt{{{1}^{2}}}} \right)\] \[\Rightarrow \]               \[x-3=\pm (y-4)\] \[\Rightarrow \]               \[x-y+1=0\] \[\Rightarrow \]