To find the distance between the points \( (9, 1) \) and \( (-3, 6) \), we can use the distance formula, which is given by
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we set:
- \( (x_1, y_1) = (9, 1) \)
- \( (x_2, y_2) = (-3, 6) \)
Now, we substitute the coordinates into the formula:
\[ d = \sqrt{((-3) - 9)^2 + (6 - 1)^2} \]
Calculating \( (-3) - 9 \) gives us:
\[ -3 - 9 = -12 \]
Now, squaring it:
\[ (-12)^2 = 144 \]
Next, we calculate \( 6 - 1 \):
\[ 6 - 1 = 5 \]
Now, squaring this value:
\[ 5^2 = 25 \]
Now, we substitute these squared values back into the distance formula:
\[ d = \sqrt{144 + 25} \]
Adding the two values inside the square root:
\[ 144 + 25 = 169 \]
Taking the square root gives us:
\[ d = \sqrt{169} = 13 \]
Thus, the distance between the points \( (9, 1) \) and \( (-3, 6) \) is
\[ \boxed{13.0} \]
when rounded to the nearest tenth.
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