Question:
a) Let P and Q be two points in space, and X the midpoint of the line segment PQ.
Let O be an arbitrary ﬁxed point; show that as vectors, OX = 1/2 (OP + OQ) .

b) With the notation of part (a), assume that X divides the line segment PQ in
the ratio r : s, where r + s = 1. Derive an expression for OX in terms of OP and OQ.

Answer:
a) OX = OP + PX = OP + 1/2(PQ) = OP + 1/2(OQ−OP)= 1/2(OP + OQ)

b) OX = sOP + rOQ; replace 1/2 by r in above; use 1 − r = s.

My Question: In the answer to part b, what does "replace 1/2 by r in above; use 1 − r = s" mean? How does it help?

Question

Question:
a) Let P and Q be two points in space, and X the midpoint of the line segment PQ. 
Let O be an arbitrary ﬁxed point; show that as vectors, OX = 1/2 (OP + OQ) .

b) With the notation of part (a), assume that X divides the line segment PQ in 
the ratio r : s, where r + s = 1. Derive an expression for OX in terms of OP and OQ. 

Answer:
a) OX = OP + PX = OP + 1/2(PQ) = OP + 1/2(OQ−OP)= 1/2(OP + OQ)

b) OX = sOP + rOQ; replace 1/2 by r in above; use 1 − r = s.

My Question: In the answer to part b, what does "replace 1/2 by r in above; use 1 − r = s" mean? How does it help?