Question

Prove that the following set of point is collinear :

(5 , 1),(3 , 2),(1 , 3)

Answer 1

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.