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Question
Prove that the following set of point is collinear :
(5 , 1),(3 , 2),(1 , 3)
Solution
P (5 , 1) Q (3 , 2) R (1 , 3)
PQ = `sqrt ((5 - 3)^2 + (1 - 2)^2) = sqrt (4+1) = sqrt 5` units
QR = `sqrt ((3 - 1)^2 + (2 - 3)^2) = sqrt (4+1) = sqrt 5` units
PR = `sqrt ((5 - 1)^2 + (1 - 3)^2) = sqrt (16+4) = sqrt 20` units
PQ + QR = `sqrt 5 +sqrt 5 = 2sqrt 5 = PR`
∵ PQ + QR = PR
∵ P , Q and R are collinear points.
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