Question

Find the equation of the line passing through (1, 2) and (3, 6) using the determinant.

Answer 1

Let P(x, y) be a point on the line $\Rightarrow P(x,y),A(1,2),B(3,6)$ are collinear

$\Rightarrow \left|\begin{array}{ccc}1& 1& 1\\ x& 1& 3\\ y& 2& 6\end{array}\right|=0$
$\Rightarrow 1(6-6)-x(6-2)+y(3-1)=0$
$\Rightarrow -4x+2y=0$
$\Rightarrow y=2x$