Question
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Question
If you want to dilate an isosceles right triangle with a hypotenuse of 18 yards, to create a dilated image with a hypotenuse of 12 yards, what scale factor should you use?(1 point)
Responses
23
yard
Start Fraction 2 over 3 End Fraction yard
32
Start Fraction 3 over 2 End Fraction
6 yards
6 yards
23
Answers
GPT-4o mini
To find the scale factor for the dilation, you can use the formula:
\[
\text{Scale Factor} = \frac{\text{length of side in the image}}{\text{length of corresponding side in the original}}
\]
In this case, you want to dilate an isosceles right triangle with a hypotenuse of 18 yards to create a dilated image with a hypotenuse of 12 yards.
So, the scale factor is:
\[
\text{Scale Factor} = \frac{12 \text{ yards}}{18 \text{ yards}} = \frac{12}{18} = \frac{2}{3}
\]
Therefore, the scale factor you should use is:
**Start Fraction 2 over 3 End Fraction**
\[
\text{Scale Factor} = \frac{\text{length of side in the image}}{\text{length of corresponding side in the original}}
\]
In this case, you want to dilate an isosceles right triangle with a hypotenuse of 18 yards to create a dilated image with a hypotenuse of 12 yards.
So, the scale factor is:
\[
\text{Scale Factor} = \frac{12 \text{ yards}}{18 \text{ yards}} = \frac{12}{18} = \frac{2}{3}
\]
Therefore, the scale factor you should use is:
**Start Fraction 2 over 3 End Fraction**