Answer:
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.
![PB = \dfrac{4}{7}\times 7 = 4\ units](https://tex.z-dn.net/?f=PB%20%3D%20%5Cdfrac%7B4%7D%7B7%7D%5Ctimes%207%20%3D%204%5C%20units)
![QB = \dfrac{3}{7}\times 7 = 3\ units](https://tex.z-dn.net/?f=QB%20%3D%20%5Cdfrac%7B3%7D%7B7%7D%5Ctimes%207%20%3D%203%5C%20units)
![RB = \dfrac{5}{7}\times 7 = 5\ units](https://tex.z-dn.net/?f=RB%20%3D%20%5Cdfrac%7B5%7D%7B7%7D%5Ctimes%207%20%3D%205%5C%20units)
![SB = \dfrac{2}{7}\times 7 = 2\ units](https://tex.z-dn.net/?f=SB%20%3D%20%5Cdfrac%7B2%7D%7B7%7D%5Ctimes%207%20%3D%202%5C%20units)
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, <em>S is closest to B</em>.