Question

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

Answer 1

Let $P(x,y)$ be any point on the line joining points $A(1,2)$ and $B(3,6)$

Then, the points A, B and P are collinear. Therefore, the area of triangle ABP will be zero.

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

$\Rightarrow 6-y-6+2x+3y-6x=0$

$\Rightarrow y=2x$

Hence, the equation of the line joining the given points is $y=2x$.