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प्रश्न
Find equation of line joining (3, 1) and (9, 3) using determinant.
उत्तर
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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