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Question
Prove that the following set of point is collinear :
(5 , 5),(3 , 4),(-7 , -1)
Solution
A (5 , 5) B (3 , 4) C (-7 , -1)
AB = `sqrt ((5-3)^2 + (5-4)^2) = sqrt (4+1) = sqrt 5` units
BC = `sqrt ((3 +7)^2 + (4 + 1)^2) = sqrt (100 + 25) = 5 sqrt 5` units
AC = `sqrt ((5 +7)^2 + (5 + 1)^2) = sqrt (144 + 36) = 6 sqrt 5` units
AB + BC = `sqrt 5 + 5 sqrt 5 = 6 sqrt 5 = "AC"`
∵ AB + BC = AC
hence A,B and C are collinear points.
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