To find the distance between the points \((9,1)\) and \((-3,6)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (9, 1)\) and \((x_2, y_2) = (-3, 6)\).
Now substitute the values into the formula:
\[ d = \sqrt{((-3) - 9)^2 + (6 - 1)^2} \]
Calculating each part:
\[ d = \sqrt{(-12)^2 + (5)^2} \]
\[ d = \sqrt{144 + 25} = \sqrt{169} = 13 \]
The distance between the points is 13.0 units (rounded to the nearest tenth).
Now, to find the midpoint of the segment connecting these two points, we use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Substituting in the coordinates:
\[ \text{Midpoint} = \left( \frac{9 + (-3)}{2}, \frac{1 + 6}{2} \right) \]
Calculating each part:
\[ \text{Midpoint} = \left( \frac{6}{2}, \frac{7}{2} \right) = \left( 3, 3.5 \right) \]
Therefore, the midpoint of the segment is (3, 3.5).
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