Question

Determine if the points $(1,5),(2,3)$ and $(-2,-11)$ are collinear , by distance formula.

Answer 1

$A(1,5),B(2,3)andC(-2,-11)$

Now, $AB=\sqrt{\left(1^2\right)+\left(2^2\right)}=\sqrt{5}BC=\sqrt{\left(4^2\right)+\left({14}^2\right)}=\sqrt{212}CA=\sqrt{\left(1^2\right)+\left({16}^2\right)}=\sqrt{257}$

As,$CA>BC>AB$

If points $A,BandC$ are collinear then $AB+BC=CA$

But $\sqrt{5}+\sqrt{212}\ne \sqrt{257}$

So they are not collinear.