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Question
Using determinants, find the equation of the line joining the points
(1, 2) and (3, 6)
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Solution
Given: A = (1, 2) and B = (3, 6)
Let the point P be (x, y). So,
Area of triangle ABP = 0
\[\Rightarrow ∆ = \frac{1}{2}\begin{vmatrix}1 & 2 & 1 \\ 3 & 6 & 1 \\ x & y & 1\end{vmatrix} = 0\]
\[ \Rightarrow 1\left( 6 - y \right) - 2\left( 3 - x \right) + 1\left( 3y - 6x \right) = 0\]
\[ \Rightarrow 6 - y - 6 + 2x + 3y - 6x = 0\]
\[ \Rightarrow 2y - 4x = 0\]
\[ \Rightarrow y = 2x\]
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