Question

Find the area of triangle(in sq. units) formed by following lines
$2x-y-2=0$
$4x+3y-24=0$
$y+4=0$

Answer 1

Let the lines $2x-y-2=0$, $4x+3y-24=0$ and $x\left(0\right)+y+4=0$ forms a traingle ABC

Area of $△ABC=\frac{1}{2}\left|\begin{array}{ccc}2& -1& -2\\ 4& 3& -24\\ 0& 1& 4\end{array}\right|$

$=\left(2\right(12+24)+1(16+0)-2(4-0\left)\right)\left(\frac{1}{2}\right)$

$=40$ sq.units