Determine whether the given points are collinear.

(1) A(0,2) , B(1,-0.5), C(2,-3) are the given points.
Slope of line AB = (y₂-y₁)/ (x₂-x₁)
= (-0.5-2)/(1-0))
= -2.5/1 = -2.5
Slope of line BC = (y₂-y₁)/ (x₂-x₁)
= (-3-(-0.5))/(2-1)
= -2.5/1 = -2.5
Slope of line AB and BC are equal.
Point B lies on both lines.
Point A,B,C are collinear.

(2) P(1, 2) , Q(2, 8/5 ) , R(3, 6/5 ) are the given points.
Slope of line PQ = (y₂-y₁)/ (x₂-x₁)
= ((8/5)-2)/(2-1))
= (-2/5)/1 = -2/5
Slope of line QR = (y₂-y₁)/ (x₂-x₁)
= (6/5-(8/5))/(3-2)
=( -2/5)/1 = -2/5
Slope of line PQ and QR are equal.
Point Q lies on both lines.
Point P,Q,R are collinear.

(3) L(1,2) , M(5,3) , N(8,6) are the given points.
Slope of line LM = (y₂-y₁)/ (x₂-x₁)
= (3-2)/(5-1))
= 1/4
Slope of line MN = (y₂-y₁)/ (x₂-x₁)
= (6-3)/(8-5)
=3/3 = 1
Slope of line LM ≠ Slope of MN
Point L,M,N are not collinear.