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Question
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
Solution
Let A( -2,5) , B(0,1) and C (2, -3) be the give points. Then
`AB= sqrt((0+2)^2 +(1+5)^2 ) = sqrt((2)^2 +(-4)^2) = sqrt(20) = 2 sqrt(5) `units
`BC = sqrt((2-0)^2 + (-3-1)^2) = sqrt((2)^2+(-4)^2) = sqrt(20) = 2 sqrt(5)` units
`AC= sqrt((2+2)^2 +(-3-5)^2) = sqrt((4)^2 +(-8)^2) = sqrt(80) = 4sqrt(5) `units
`∴ AB +BC = (2 sqrt(5)+2 sqrt(5)) units = 4 sqrt(5) units = Ac`
Hence, the given points are collinear
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