To determine how long a line segment that represents 10 feet would be on the scale drawing, we first need to find the scale ratio.
We know from the information given that 2 inches on the scale represents 30 feet. To find out how many inches represent 1 foot, we can set up the following conversion:
\[ \text{Inches per foot} = \frac{2 \text{ inches}}{30 \text{ feet}} \]
Now, to find how many inches represent 1 foot, we can divide both the numerator and the denominator by 30:
\[ \text{Inches per foot} = \frac{2 \text{ inches}}{30 \text{ feet}} = \frac{2}{30} = \frac{1}{15} \text{ inches per foot} \]
This means that for every foot, the scale drawing measures \( \frac{1}{15} \) inches.
Now, we need to find out how many inches represent 10 feet:
\[ \text{Inches for 10 feet} = 10 \text{ feet} \times \frac{1}{15} \text{ inches per foot} \]
Calculating this gives:
\[ \text{Inches for 10 feet} = \frac{10}{15} = \frac{2}{3} \text{ inches} \]
Thus, a line segment that represents 10 feet on the scale drawing will be \( \frac{2}{3} \) inches long.
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