Find equation of line joining (3, 1) and (9, 3) using determinant… - Vidyadip

Question

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

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Answer

Let $(x, y)$ be any point on the line containing $(3, 1)$ and $(9, 3),$ then the required equation is,$\left| {\begin{array}{*{20}{c}} \begin{gathered} x \hfill \\ 3 \hfill \\ 9 \hfill \\ \end{gathered} &\begin{gathered} y \hfill \\ 1 \hfill \\ 3 \hfill \\ \end{gathered} &\begin{gathered} 1 \hfill \\ 1 \hfill \\ 1 \hfill \\ \end{gathered} \end{array}} \right| = 0$
Expanding along $R_1 ,$ we get,
$x[1-3]-y[3-9]+1[9-9]=0$
$\Rightarrow -2x+6y=0$
$ x=3y$ which is the required equation of the line.

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