Question

Find the equation of line passing through the points $(3,2)$ and $(-1,3)$ by using determinants.

Answer 1

Equation of line through $(3,2)$ & $(-1,3)$ is

$\left|\begin{array}{cc}x-3& y-2\\ -1-3& 3-2\end{array}\right|=0$

$\Rightarrow \left|\begin{array}{cc}x-3& y-2\\ -4& 1\end{array}\right|=0$

$x-3+4(y-2)=0$

$\Rightarrow x+4y=11$