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Question
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
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Solution
Let A (1,-1), B(5,2) and C(9,5) be the give points. Then
`AB= sqrt((5-1)^2 +(2+1)^2 ) = sqrt(4^2+3^2) = sqrt(25) = 5` unts
`BC = sqrt((9-5)^2 +(5-2)^2 ) = sqrt((4^2+3^2)) = sqrt(25)` = 5 units
`AC= sqrt((9-1)^2 +(5+1)^2) = sqrt(8^2+6^2) = sqrt(100)`=10 unit
∴ AB+BC = (5+5) units = 10 units = AC
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