Question

In $△ABC$, the equations of bisectors of angles $B,C$ are $x-y=0,y=0$. If $A=(2,1)$ then the equation of $BC$ is

• A. $3x+y=5$
• B. $x+y=3$
• C. $x+2y=4$
• D. $x+y=4$

Answer 1

The correct option is A $3x+y=5$

$\text{If we take image of}A\text{about}$

$\text{both the angle bisectors of}\angle B\text{and}\angle C$

$\text{then we will get vertex}C\text{and}B\text{.}$

Image of $A\equiv (2,1)$ in $x=y$ is (1,2)

Image of $A\equiv (2,L)$ in $y=0$ is (2,-1)

Equation of line BC can lie written as

$\frac{y+1}{x-2}=\frac{y-2}{x-1}$

$\Rightarrow xy-y+x-1=xy-2x-2y+4$

$\Rightarrow y+3x-5=0$

so equation of line $BC$ is $3x+y=5$

Answer: option (A)