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 R₁ , 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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