Find equation of line joining (1, 2) and (3, 6) using determinant… - Vidyadip

Question

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

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Answer

Let P (x, y) be any points on the line joining the points (1, 2) and (3, 6).
Then, Area of triangle that could be formed by these points is zero.
$\therefore\ \ \text{Area of triangle}=\text{Modulus of}\ \frac{1}{2}\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix}=0$
$\Rightarrow\ \text{Modulus of}\ \frac{1}{2}\begin{vmatrix}x&y&1\\1&2&1\\3&6&1\end{vmatrix}=0$
$\Rightarrow\ \frac{1}{2}\left[x(2-6)-y(1-3)+1(6-6)\right]=0$
$\Rightarrow\ \ -4x+2y=0\ \Rightarrow\ \ -2x+y=0$
$\Rightarrow\ \ y=2x$ Which is required line.

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