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

S

Reason: If a point divides AB in the ratio m:n (AP:PB = m:n), PB = n/(m+n) of AB. For P, Q, R, S the PB fractions are 4/7, 3/7, 5/7, 2/7 respectively, so S (2/7) is closest to B.