Straight lines question

Question

In a triangle $ABC$, the bisectors of angles $B$ and $C$ lie on lines $x=y$ and $y=0$. If $A$ is $(1,2)$ then equation of $BC$ is?

Answer 1

The image of $A$ with respect to the angle bisectors of $B$ and $C$ will lie on the line $BC$. This can be deducted from the definition of an angular bisector.

Hence, Image of $ (1,2) $ in $ x = y $ is $ (2,1) $. And Image of $ (1,2) $ in $ y = 0 $ is $ (1,-2) $.

Both of these points will lie on BC.

Hence its formula is :

$ 3x-y-5=0 $