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

To find:  if the points (1,5) (2,3) and (−2,−11) are collinear.

Solution:

Let A = (1, 5), B = (2, 3) and C = (- 2,-11)

So The distance AB :

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

$AB=\sqrt{1+4}$

$AB=\sqrt{5}$

The distance BC :

$BC=\sqrt{(-2-2)^2+(-11-3)^2}$

$BC=\sqrt{16+196}$

$BC=\sqrt{212}$

The distance CA :

$CA=\sqrt{(1-(-2))^2+(5-(-11))^2}$

$CA=\sqrt{9+256}$

$CA=\sqrt{265}$

As we can see that  

AB + BC ≠ CA

Therefore, the points (1, 5), (2, 3), and ( - 2, - 11) are not collinear.

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Updated on: 10-Oct-2022

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