# 3. Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

D Divya Prakash Singh

Let the points (1, 5), (2, 3) and (– 2, – 11) be representing the vertices A, B, and C of the given triangle respectively.

$A = (1,5),\ B = (2,3),\ C = (-2,-11)$

Therefore,

$AB = \sqrt{(1-2)^2+(5-3)^2} = \sqrt{5}$

$BC = \sqrt{(2-(-2))^2+(3-(-11))^2} = \sqrt{4^2+14^2} = \sqrt{16+196} = \sqrt{212}$$CA = \sqrt{(1-(-2))^2+(5-(-11))^2} = \sqrt{3^2+16^2} = \sqrt{9+256} = \sqrt{265}$Since these are not satisfied.

$AB+BC \neq CA$

$BA+AC \neq BC$

$BC+CA \neq BA$

As these cases are not satisfied.

Hence the points are not collinear.

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