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Question
Find equation of line joining (3, 1) and (9, 3) using determinant.
Solution
Let P(x, y) be the point on the line joining the points A(3, 1) and B(9, 3). Then the points A, P and B are collinear.
∴ Area (∆ APB) = 0
`=> 1/2 abs ((3,1,1),(9,3,1),(x,y,1)) = 0`
`=> abs ((3,1,1),(9,3,1),(x,y,1)) - 0`
⇒ x (1 - 3) - y (3 - 9) + 1 (9 - 9) = 0
⇒ -2x + 6y = 0
⇒ x - 3y = 0
Hence, x - 3y = 0 is the required line.
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