Respuesta :
The difference between partitioning into a ratio of 1/2 and finding half of a line segment is that partitioning in that ratio means one part is longer than the other, whereas finding half the length means both parts are the same length.
What is the partition of the line?
Partition means to separate or to divide. A line segment can be partitioned into smaller segments which are compared as ratios.
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 total number of parts 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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Because 1:2 is not a fraction while 1/2 is, you cannot assume that 1:2 is one-half of a line or anything that is being delt with in fact. The length of the line might be 18 units, and if it says that there needs to be some sort of action with a ratio of 1:2, you are not splitting that length in half, you are taking one unit from the left side, and two from the right, which does not equal the length of half of 18 units.
