Question

Find the equation of the line joining $A(1,3)$ and $B(0,0)$ using determine and find $k$ of $D(k,0)$ is a point such that area of $△$ $ABD$ is $3$ sq. units.

Answer 1

$A(1,3)B(0,0)D(k,0)$

$△=\left|\begin{array}{ccc}1& 1& 1\\ 1& 0& k\\ 3& 0& 0\end{array}\right|$

$△=1(0-0)-1(0-3k)+1(0-0)$

$△=3k$

Area$=\frac{1}{2}\left|△\right|=3$

$3k=\pm 6$

$\Rightarrow k=\pm 2$