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]
