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

Question

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 (A) 4 (B) 2 (C) -2 (D) -4

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-bvvcummza2xi.png" /> Reflection of A(2,3) about line y+x=0 is A'(- 3 , - 2) which lies on side BC ⇒ 2(- 3)-5(- 2)+a=0⇒ a=-4

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

$4$

$2$

$- 2$

$- 4$

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

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

4

2

−2

−4

Reflection of A(2,3) about line y+x=0 is A′(−3,−2) which lies on side BC ⇒ 2(−3)−5(−2)+a=0⇒a=−4

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

$4$

$2$

$- 2$

$- 4$

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