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प्रश्न
Prove that the following set of point is collinear :
(4, -5),(1 , 1),(-2 , 7)
उत्तर
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.
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