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Question
Using determinants, find the equation of the line joining the points
(3, 1) and (9, 3)
Solution
Given: A = (3, 1) and B = (9, 3)
Let the point P be (x, y). So,
Area of triangle ABP = 0
\[\Rightarrow ∆ = \frac{1}{2}\begin{vmatrix}3 & 1 & 1 \\ 9 & 3 & 1 \\ x & y & 1\end{vmatrix} = 0\]
\[ \Rightarrow 3\left( 3 - y \right) - 1\left( 9 - x \right) + 1\left( 9y - 3x \right) = 0\]
\[ \Rightarrow 9 - 3y - 9 + x + 9y - 3x = 0\]
\[ \Rightarrow - 2x + 6y = 0\]
\[ \Rightarrow x = 3y\]
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