Question

Determine whether the following points are collinear.

i. A (-1, -1), B (0, 1), C (1, 3) 

ii. D (- 2, -3), E (1, 0), F (2, 1) 

iii. L (2, 5), M (3, 3), N (5, 1) 

iv. P (2, -5), Q (1, -3), R (-2, 3) 

v. R (1, -4), S (-2, 2), T (-3, 4)

vi. A(-4, 4),K[-2, 5/2], N (4,-2)

Answer 1

∴ 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.

∴ 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.

∴ slope of line LM ≠ slope of line MN 

∴ Points L, M and N are not collinear.

∴ slope of line PQ = slope of line QR 

∴ line PQ || line QR 

Also, point Q is common to both the lines. 

∴ Both lines are the same. 

∴ Points P, Q and R are collinear.

∴ slope of line RS = slope of line ST 

∴ line RS || line ST

Also, point S is common to both the lines.

∴ Both lines are the same. 

∴ Points R, S and T are collinear.

∴ slope of line AK = slope of line KN 

∴ line AK || line KN 

Also, point K is common to both the lines. 

∴ Both lines are the same. 

∴ Points A, K and N are collinear.