Explain the difference between partitioning a directed line segment {MN} in a 2:7 ratio versus a 7:2 ratio. Include a specific example as part of your explanation.
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The difference between partitioning a directed line segment {MN} in a 2:7 ratio versus a 7:2 ratio can be explained as follows.
- Suppose the line MN which is of definite length is divided into 9 equal parts. Here, we are dividing it into nine parts because the proportions 2 and 7 make a sum of 9.
- When the line is divided in the ratio 2:7, the first two parts out of the nine from the left side are separated from the rest 7. This means that the first proportion from the left side of the line is smaller than the other.
- Now, when the line is divided in the ratio 7:2, the first seven parts out of the nine from the left side are separated from the rest two. This means that the first proportion from the left side of the line is larger than the other.
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