Question

Determine whether the points are collinear. 

i. R (0, 3), D (2, 1), S (3, -1) 

ii. P (-2, 3), Q (1, 2), R (4, 1)

Answer 1

i. By distance formula,

On adding (i) and (ii), 

∴ d(R, D) + d(D, S) = √8 + √5 ≠ 5

∴ d(R, D) + d(D, S) ≠ d(R, S) … [From (iii)] 

∴ Points R, D and S are not collinear.

∴ d(R, D) + d(D, S) ≠ d(R, S) … [From (iii)] 

∴ Points R, D and S are not collinear.

ii. By distance formula,

∴ d(P, R) = 2√10    ....(iii)

On adding (i) and (ii), 

d(P, Q) + d(Q, R) = √10 + √10 = 2√10 

∴ d(P, Q) + d(Q, R) = d(P, R) … [From (iii)] 

∴ Points P, Q and R are collinear.