Show that the points (1,2), (2,1), (-2,5) lie on the same line i.e., collinear.

Given points (1,2)(2,1)(-2,5)

For there points to be collinear it is sufficient to prove BA+AC=BC

$Let A(1,2)B(2,1)(-2,5)$

$BA=\sqrt{\left(\right(2-1{)}^2+(1-2{)}^2)}=\sqrt{(P^2+12)}=\sqrt{2}$

$AC=\sqrt{\left(\right(1-(-2{)}^2+(2-5{)}^2}=\sqrt{18}=3\sqrt{2}$

$BC=\sqrt{\left(\right(2-(-2){)}^2+(1-5{)}^2)}=\sqrt{32}=4\sqrt{2}$

$BA+BC=\sqrt{2}+3\sqrt{2}=4\sqrt{2}=BC.$

Hence the 3 points A,B,C are collinear.
Hence proved
formula: d= distance $=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$