To determine if Mya made an error in calculating the scale factor, let's consider each given explanation and analyze it step-by-step.
### Step-by-Step Analysis
1. Understanding the Correct Method for Calculating Scale Factor:
- The scale factor is calculated by comparing the dimensions of the original figure with the dimensions of the scaled figure.
- Specifically, the scale factor is found by multiplying the dimensions in a manner that maintains proportionality.
2. Identifying the Incorrect Method Mya Might Have Used:
- If Mya calculated the scale factor as 1/2, it suggests she may have performed an incorrect operation.
3. Possible Errors Mya Might Have Made:
- Mya only used the dimensions from the scale drawing of a rectangle:
- This would mean that Mya did not consider the original dimensions when calculating the scale factor.
- Without comparing the original and the scaled dimensions, this calculation method is clearly flawed.
- Mya used the 10 ft side and the 8 ft side as corresponding sides:
- If the 10 ft side corresponds to 8 ft in the scaled figure, using these incorrectly matched sides would lead to an incorrect calculation.
- Corresponding sides must match in the original and scaled figures.
- Mya divided the dimensions, instead of multiplying them, to find the scale factor:
- Typically, to find the scale factor, you should multiply or compare dimensionally equivalent sides, not divide.
- If Mya divided the dimensions, it shows she used an incorrect operation.
- Mya did not make an error when she calculated the scale factor:
- If this statement were true, the calculated scale factor should align correctly with the given dimensions and methodology.
4. Evaluating the Division as Mya's Error:
- Mya might have divided corresponding dimensions to find the scale factor.
- If 8 ft was divided by 10 ft, the result is [tex]\( \frac{8}{10} = 0.8 \)[/tex], which is not [tex]\( \frac{1}{2} \)[/tex]. Calculating the factor correctly by similar or proportional methods should result in a commendable value.
Conclusion:
- Mya’s calculated scale factor of [tex]\( \frac{1}{2} \)[/tex] being inaccurate suggests she might have divided instead of using the appropriate methodology. Thus, the error Mya could have made when she calculated the scale factor is:
"Mya divided the dimensions, instead of multiplying them, to find the scale factor."
This process leaves room for understanding where Mya went wrong and encourages fixing the calculative approach for accurate results.
