Question

Four points partition the directed line segment from A to B.

• Point P partitions the directed line segment from A to B into a 3:4 ratio.
• Point Q partitions the directed line segment from A to B into a 4:3 ratio.
• Point R partitions the directed line segment from A to B into a 2:5 ratio.
• Point S partitions the directed line segment from A to B into a 5:2 ratio.

A number line has points A and B. A line is drawn from point A to point B.

Which point will lie closest to B?

P
Q
R
S

Answer 1

If AP:PB = m:n then PB = n/(m+n)·AB.

So:
- P: PB = 4/7 AB
- Q: PB = 3/7 AB
- R: PB = 5/7 AB
- S: PB = 2/7 AB

The smallest distance to B is 2/7 AB, so S is closest to B.