Question

Prove that the following set of point is collinear :

(5 , 5),(3 , 4),(-7 , -1)

Answer 1

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.