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Question
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
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Solution
Let A( 6,9) ,B( 0,1 ) and C (-6, -7) be the give points. Then
`AB = sqrt((0-6)^2 +(1-9)^2 )= sqrt((-6)^2 +(-8)^2) = sqrt(36 + 64)= sqrt(100)`=10 units
`BC=sqrt((-6-0)^2+(-7-1)^2) = sqrt((-6)^2+(-8)^2)= sqrt(36 + 64)= sqrt(100) `=10 units
`AC = sqrt((-6-6)^2 +(-7-9)^2 )= sqrt((-12)^2 +(16)^2) = sqrt(144 + 256 )= sqrt(400)`= 20 units
∴ AB + BC = (10+10) units - 20 units = AC
Hence, the given points are collinear
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