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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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