To find the scale factor for dilating an isosceles right triangle, you can use the following formula for scale factor (k):
\( k = \frac{\text{new length}}{\text{original length}} \)
In this case, the original hypotenuse is 18 yards and the new hypotenuse is 12 yards. Plugging in these values:
\( k = \frac{12}{18} \)
To simplify this fraction:
\( k = \frac{2}{3} \)
So the scale factor you should use is \( \frac{2}{3} \).
Therefore, the correct answer is:
Start Fraction 2 over 3 End Fraction.