i. Given, d(P, R) = 7, d(P, Q) = 10, d(Q, R) = 3 

d(P, Q) = 10 …(i) 

d(P, R) + d(Q, R) = 7 + 3 = 10 .. .(ii) 

∴ d(P, Q) = d(P, R) + d(Q, R) …[From (i) and (ii)] 

∴ Point R is between the points P and Q 

i. e., P – R – Q or Q – R – P. 

∴ Points P, R, Q are collinear. 

ii. Given, d(R, S) = 8, d(S, T) = 6, d(R, T) = 4 

d(R, S) = 8 …(i) 

d(S, T) + d(R, T) = 6 + 4 = 10 …(h) 

∴ d(R, S) ≠ d(S, T) + d(R, T) … [From (i) and (ii)] 

∴ The given points are not collinear.

iii. Given, d(A, B) = 16, d(C, A) = 9, d(B, C) = 7 

d(A, B) = 16 …(i) 

d(C, A) + d(B, C) = 9 + 7 = 16 …(ii) 

∴ d(A, B) = d(C, A) + d(B, C) …[From(i) and (ii)] 

∴ Point C is between the points A and B.

i. e., A – C – B or B – C – A. 

∴ Points A, C, B are collinear 

iv. Given, d(L, M) = 11, d(M, N) = 12, d(N, L) = 8 

d(M, N) = 12 …(i) 

d(L, M) + d(N, L) = 11 + 8 = 19 …(ii) 

∴d(M, N) + d(L, M) + d(N, L) … [From (i) and (ii)] 

∴ The given points are not collinear.

v. Given, d(X, Y) = 15, d(Y, Z) = 7, d(X, Z) = 8 

d(X, Y) = 15 …(i) 

d(X,Z) + d(Y, Z) = 8 + 7= 15 …(ii) 

∴ d(X, Y) = d(X, Z) + d(Y, Z) …[From (i) and (ii)] 

∴ Point Z is between the points X and Y 

i. e.,X – Z – Y or Y – Z – X. 

∴ Points X, Z, Y are collinear. 

vi. Given, d(D, E) = 5, d(E, F) = 8, d(D, F) = 6 

d(E, F) = 8 …(i)

d(D, E) + d(D, F) = 5 + 6 = 11 …(ii) 

∴ d(E, F) ≠ d(D, E) + d(D, F) … [From (i) and (ii)] 

∴ The given points are not collinear.