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

The closest point to point B on the line AB is point S

The ratios are given as:

P = 3 : 4

Q = 4 : 3

R = 2 : 5

S = 5 : 2

Given that the point is from A to B, the first ratio proportion represents the position of each point between A and B

So, we remove the second ratio proportion of the above ratios

P = 3

Q = 4

R = 2

S = 5

The point with the highest value is S i.e. 5

Hence, point S is the closest to point B

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S is closest to B.

Step-by-step explanation:

Given a directed line segment from point A to B.

Point P divides the line A to B in a ratio 3:4.

Point Q divides the line A to B in a ratio 4:3.

Point R divides the line A to B in a ratio 2:5.

Point S divides the line A to B in a ratio 5:2.

To find:

The point which is closest to the point B.

Solution:

Here, to find the point closest to B we need to find the distances PB, QB, RB and SB.

We can see the sum of ratio 3:4, 4:3, 2:5 and 5:2 is 7.

Let the distance between A and B be 7 units.

Now, the distances can be found easily.

The point which has the minimum distance from point B, will be nearest to B.

We can clearly observe that SB is the minimum distance.

Therefore, S is closest to B.