The reason why partitioning into a ratio of 1:2 and finding half of the line segment is not the same is because; partitioning in that ratio means one part is longer than the other while half the length means that both parts are the same length.
- When we say we want to partition a line into a ratio of say x:y, it means that the line has been divided in that ratio and as such the the total number of parts of is x + y.
- Similarly, when we partition a line in the ratio 1:2, it implies that the total number of parts of the line segment is 1 + 2 = 3.
This means one part of the divided segment is bigger than the other one.
In contrast, half of the line segment means that the line segment is divided into two equal parts.
Thus, the fundamental difference between partitioning into a ratio of 1:2 and finding half of the line segment is that partitioning in that ratio means one part is longer than the other while half the length means that both parts are the same length.
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