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Question
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Solution
Let A(-1, -1) , B(2,3) and C( 8,11) be the give points. Then
`AB = sqrt((2+1)^2 +(3+1)^2) = sqrt((3)^2 +(4)^2) = sqrt(25)` =5 units
`BC=sqrt((8-2)^2 +(11-3)^2 = sqrt(6)^2 +(8)^2 = sqrt(100) `= 10 units
`AC = sqrt(( 8+1)^2 +(11+1)^2 ) = sqrt((9)^2 +(12)^2 = sqrt(225) `= 15 units
∴ AB +BC = (5+10) units = 15 units = Ac
Hence, the given points are collinear
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