Question

Find the equation of line joining (1, 2) and (3, 6) using determinants.

Answer 1

We have to find the equation of line joining $(1,2)$ and $(3,6)$

Let the third point on the line be $(x,y)$

The area of triangle with vertices $(x,y),(1,2),(3,6)$ is $\frac{1}{2}\left|\begin{array}{ccc}x& y& 1\\ 1& 2& 1\\ 3& 6& 1\end{array}\right|$

Since the three points are collinear, the area formed will be zero

$⟹\left|\begin{array}{ccc}x& y& 1\\ 1& 2& 1\\ 3& 6& 1\end{array}\right|=0$

$⟹x(2-6)-y(1-3)+1(6-6)=0$

$⟹-4x+2y=0$

$⟹2x-y=0$.

Hence, the equation of line joining $(1,2)$ and $(3,6)$ is $2x-y=0$.