i. Slope of line AB = (y2 - y1)/(x2 - x1)
= (1-(-1))/(0 - (-1)) = (1 + 1)/(0 + 1) = 2
Slope of line BC = (y2 - y1)/(x2 - x1)
= (3-1)/(1 - 0) = 2
∴ slope of line AB = slope of line BC
∴ line AB || line BC
Also, point B is common to both the lines.
∴ Both lines are the same.
∴ Points A, B and C are collinear.
ii. Slope of line DE = (y2 - y1)/(x2 - x1)
= (0 - (-3))/(1-(-2))
= (0 + 3)/(1 + 2) = 3/3 = 1
Slope of line EF = (y2 - y1)/(x2 - x1)
= (1 - 0)/(2 - 1) = 1
∴ slope of line DE = slope of line EF
∴ line DE || line EF
Also, point E is common to both the lines.
∴ Both lines are the same.
∴ Points D, E and F are collinear