Question

$A(5,4),B(-3,-2)$ and $C(1,-8)$ are the vertices of a triangle ABC. The respective equations of the median AD and the line $l$ parallel to AC passing through point $B$ are

• A. $3x+2y-7=0$ & $3x+y+7=0$
• B. $3x-2y+7=0$ & $3x-y+7=0$
• C. $3x-2y-7=0$ & $3x-y+7=0$
• D. $3x+2y-7=0$ & $3x-y-7=0$

Answer 1

The correct option is C $3x-2y-7=0$ & $3x-y+7=0$

At first for median through $A$ ie, $AD$, $D=(-1,-5)${mid point of $BC$}

$\therefore$Equation of AD : $y+5=\frac{3}{2}(x+1)$

$\therefore 3x-2y=7$

Now, line from B parallel To AC would be, $B=(-3,-2),m=m_{AC}=\frac{12}{4}=3$

$\therefore Eq:y+2=3(x+3)$

$3x-y+7=0$