Using determinants, find the equation of the line joining the poi… - Vidyadip

Question

Using determinants, find the equation of the line joining the points:
$(3, 1)$ and $(9, 3)$

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Answer

Let $A(x, y), B(3, 1)$ and$ C(9, 3)$ are $3$ points in a line.
Since these points are collinear, hence the area of the triangle ABC must be zero.
$\frac{1}{2}\begin{vmatrix}\text{x}&\text{y}&1\\3&1&1\\9&3&1\end{vmatrix}=0$
Expanding along $R_1$
$\Rightarrow x(-2) - y(-6) + 1(0) = 0$
$\Rightarrow -2x + 6y = 0$
$\Rightarrow x - 3y = 0$
Hence the equation of the line is $x - 3y = 0$

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