Answered

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



Answer :

GinnyAnswer
To determine the ratio in which point [tex]\( P \)[/tex] partitions the directed line segment from [tex]\( M \)[/tex] to [tex]\( N \)[/tex], given that [tex]\( P \)[/tex] is [tex]\(\frac{9}{11}\)[/tex] of the distance from [tex]\( M \)[/tex] to [tex]\( N \)[/tex]:

1. Understanding the partition:
- Given [tex]\( P \)[/tex] is [tex]\(\frac{9}{11}\)[/tex] of the distance from [tex]\( M \)[/tex] to [tex]\( N \)[/tex], we need to understand how many segments or parts from [tex]\( M \)[/tex] this represents relative to the total distance between [tex]\( M \)[/tex] and [tex]\( N \)[/tex].

2. Segment interpretation:
- The line can be thought of as being divided into 11 equal parts.
- Out of these 11 parts, point [tex]\( P \)[/tex] is located 9 parts from [tex]\( M \)[/tex].

3. Remaining segments calculation:
- Since [tex]\( P \)[/tex] is 9 parts from [tex]\( M \)[/tex], to find the remaining segments to reach [tex]\( N \)[/tex], we subtract the 9 parts from the total of 11 parts.

[tex]\[ \text{Remaining segments to } N = 11 - 9 = 2 \][/tex]

4. Ratio formation:
- The distance from [tex]\( M \)[/tex] to [tex]\( P \)[/tex] is 9 parts.
- The distance from [tex]\( P \)[/tex] to [tex]\( N \)[/tex] is 2 parts.
- Therefore, the ratio that point [tex]\( P \)[/tex] partitions the line segment from [tex]\( M \)[/tex] to [tex]\( N \)[/tex] into is [tex]\( 9:2 \)[/tex].

So the correct ratio is [tex]\( 9:2 \)[/tex].

Other Questions