Determine whether the following points are collinear.

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

(2) D(-2, -3), E(1, 0), F(2, 1) are the given points.
Slope of line DE = (y₂-y₁)/ (x₂-x₁)
= (0-(-3))/(1-(-2))
= 3/3 = 1
Slope of line EF = (y₂-y₁)/ (x₂-x₁)
= (1-0)/(2-1)
= 1/1 = 1
Slope of line DE and EF are equal.
Point E lies on both lines.
Point D,E,F are collinear.

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