Question

(i) Find equation of line joining $(1,2)$ and $(3,6)$ using determinants
(ii) Find equation of line joining $(3,1)$ and $(9,3)$ using determinants.

Answer 1

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

So, these points are collinear.

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

$\Rightarrow x(2-6)-y(1-3)+1(6-6)=0$

$\Rightarrow -4x+2y=0$

So, the equation of line joining the points $(1,2)$ and $(3,6)$ is $-4x+2y=0$

(ii) Let $P(x,y)$ be any point on the line joining the points $(3,1)$ and $(9,3)$

So, these points are collinear.

$\Rightarrow \left|\begin{array}{ccc}x& y& 1\\ 3& 1& 1\\ 9& 3& 1\end{array}\right|=0$

$\Rightarrow x(1-3)-y(3-9)+1(9-9)=0$

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

So, the equation of line joining the points $(3,1)$ and $(9,3)$ is $-2x+6y=0$