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  4. Let the equations of side BC and the internal angle bisector of angle B of Δ ABC are 2x-5y+a=0 and y+x=0 respectively. If A=(2,3) , then the value of a is equal to

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Q. Let the equations of side $BC$ and the internal angle bisector of angle $B$ of $\Delta ABC$ are $2x-5y+a=0$ and $y+x=0$ respectively. If $A=\left(2,3\right)$ , then the value of $a$ is equal to

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
Reflection of $A\left(2,3\right)$ about line $y+x=0$ is $A'\left(- 3 , - 2\right)$ which lies on side $BC$
$\Rightarrow $ $2\left(- 3\right)-5\left(- 2\right)+a=0\Rightarrow a=-4$