Question

The equations of the sides AB, BC and CA of $\Delta ABC$ 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 equation of the sides AB, BC and CA of $\Delta ABC$ are $y-x=2,x+2y=1$ and $3x+y+5=0,$ respectively.

Solving the equation of AB and BC, i.e.

$y-x=2$ and $x+2y=1,$ we get : $x=-1,y=1$

So, the coordinates of B are $(-1,1)$ The altitude through B is perpendicular to AC.

$\therefore$ Slope of $AC=-3$

Thus, slope of the altitude through B is $\frac{1}{3}$

Equation of the required altitude is given below :

$y-1=\frac{1}{3}(x+1)$

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