Final answer:
To partition a line segment into two segments with a length ratio of 2:9, divide the line segment into 11 equal parts. This step reflects the sum of the ratio (2+9), allowing for a correct partitioning that achieves the 2:9 ratio.
Step-by-step explanation:
To partition a line segment into two segments with a length ratio of 2:9, the line segment must be divided so that the sum of the parts reflects this ratio. The first step would be to determine the total number of equal parts the segment should be divided into to maintain that ratio. Since the ratio is 2 to 9, the sum of these parts would be 2 + 9, which equals 11.
Therefore, the correct first step would be to divide the line segment into 11 equal parts. Each part would then represent one unit of the desired ratio. Two units would create one segment, and nine units would create the second segment, thus creating two segments with lengths in the ratio 2:9.
To relate this to other concepts, when you are given other ratios such as in scales or maps, you set these ratios equal to the unit scale to form proportions. For example, a length scale/actual in inches/feet of 1/20 would mean that one inch on the scale represents 20 feet in actual length. If you were given the scale length and asked to find the actual length, you would set up a proportion and solve. Similarly, when partitioning a line segment, you use the same principle of a ratio to determine how to divide the line segment.