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If point [tex]\( P \)[/tex] is [tex]\(\frac{9}{11}\)[/tex] of the distance from [tex]\( M \)[/tex] to [tex]\( N \)[/tex], what ratio does point [tex]\( P \)[/tex] partition the directed line segment from [tex]\( M \)[/tex] to [tex]\( N \)[/tex] into?

A. 9:2
B. [tex]\( 9:9 \)[/tex]
C. 9:11
D. [tex]\( 9:13 \)[/tex]

Sagot :

GinnyAnsweridn
To determine the ratio in which point P partitions the directed line segment from M to N, we need to understand the given condition:

Point P is [tex]\(\frac{9}{11}\)[/tex] of the distance from M to N.

This means that P divides the line segment such that:
- The distance from M to P is 9 parts.
- The distance from P to N is the remaining part to complete the whole distance between M and N.

Since the total distance between M and N is divided into 11 parts (as per the denominator in the fraction [tex]\(\frac{9}{11}\)[/tex]), the remaining part from P to N would be:
[tex]\[ 11 - 9 = 2 \][/tex]

Thus, the distances from M to P and P to N are in the ratio:
[tex]\[ 9:2 \][/tex]

This ratio represents the segments formed by point P which partitions the line segment from M to N.

Therefore, the correct ratio in which point P partitions the directed line segment from M to N is:
[tex]\[ 9:2 \][/tex]
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