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.

which point will lie closest to b?

p

q

r

s

You have ratios 3:4, 4:3, 2:5 and 5:2. Each of these ratios is such that in total gives 7.

Divide segment AB in seven equal parts. Then:

Point P partitions the directed line segment from A to B into a 3:4 ratio. This means that point P lies three such parts to the right from point A and four such parts to the left from point B.Point Q partitions the directed line segment from A to B into a 4:3 ratio. This means that point Q lies four such parts to the right from point A and three such parts to the left from point B.Point R partitions the directed line segment from A to B into a 2:5 ratio. This means that point R lies two such parts to the right from point A and five such parts to the left from point B.Point S partitions the directed line segment from A to B into a 5:2 ratio. This means that point S lies five such parts to the right from point A and two such parts to the left from point B.

As you can see the closest point to point B is point S, because it lies 2 parts to the left from point B and and this amount of parts is the smallest one.

correct choice is point S.