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.
[tex]PB = \dfrac{4}{7}\times 7 = 4\ units[/tex]
[tex]QB = \dfrac{3}{7}\times 7 = 3\ units[/tex]
[tex]RB = \dfrac{5}{7}\times 7 = 5\ units[/tex]
[tex]SB = \dfrac{2}{7}\times 7 = 2\ units[/tex]
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.
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
Read more about ratios and proportions at:
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