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Using distance formula, prove that the points $A(2, 3)$, $B(-7, 0)$ and $C(-1, 2)$ are collinear.
Using distance formula, prove that the points $A(2, 3)$, $B(-7, 0)$ and $C(-1, 2)$ are collinear.
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Sol. $AB = \sqrt{(-7 - 2)^2 + (0 - 3)^2} = \sqrt{90} = 3\sqrt{10}$ (I Mark)
$BC = \sqrt{(-1 + 7)^2 + (2 - 0)^2} = \sqrt{40} = 2\sqrt{10}$ (II Mark)
$AC = \sqrt{(-1 - 2)^2 + (2 - 3)^2} = \sqrt{10}$ (III Mark)
$AC + BC = AB$
$\therefore A, B, C$ are collinear. (IV Mark)
$BC = \sqrt{(-1 + 7)^2 + (2 - 0)^2} = \sqrt{40} = 2\sqrt{10}$ (II Mark)
$AC = \sqrt{(-1 - 2)^2 + (2 - 3)^2} = \sqrt{10}$ (III Mark)
$AC + BC = AB$
$\therefore A, B, C$ are collinear. (IV Mark)