Question

The equations of the sides AB,BC and CA of the $△$ ABC are $y-x=2,x+2y=1$ and $3x+y+5=0$ respectively.The equation of the altitude through B is

• A. $x-3y+1=0$
• B. $x-3y+4=0$
• C. $3x-y+2=0$
• D. none of these

Answer 1

The correct option is B $x-3y+4=0$

The altitude through $B$ will be perpendicular to side $AC$ and will pass through the point $B$,

To get point $B$ solve line $AB$ and $BC$ $\Rightarrow B=(-1,1)$

Now slope of line $AC$ is $m=-3$

So slop of altitude will be $=-\frac{1}{m}=\frac{1}{3}$

Hence required line is, $(y-1)=\frac{1}{3}(x+1)$

$\Rightarrow x-3y+4=0$