Question

Prove that the following set of point is collinear :

(4, -5),(1 , 1),(-2 , 7)

Answer 1

M (4, -5) N (1 , 1)  S (-2 , 7)

MN = `sqrt ((4 - 1)^2 + (-5 - 1)^2) = sqrt (9+36) = 3 sqrt 5` units

NS = `sqrt ((1 + 2)^2 + (1 - 7)^2) = sqrt (9 + 36) = 3 sqrt 5` units

MS = `sqrt ((4 + 2)^2 + (-5-7)^2) = sqrt (36 + 144) = 6 sqrt 5` units

MN + NS = `3 sqrt 5 + 3 sqrt 5 = 6 sqrt 5 =` MS

∵ MN + NS = MS

∵ M , N and S are collinear points.