To calculate 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, \((x_1, y_1) = (9, 1)\) and \((x_2, y_2) = (-3, 6)\). Plugging these values into the formula:
\[ d = \sqrt{((-3) - 9)^2 + (6 - 1)^2} \] \[ = \sqrt{(-12)^2 + (5)^2} \] \[ = \sqrt{144 + 25} \] \[ = \sqrt{169} \] \[ = 13 \]
So, the distance between the two points is \(13.0\) (rounded to the nearest tenth).
Next, to find the midpoint of the segment connecting the two points, we use the midpoint formula:
\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Substituting the values:
\[ \left( \frac{9 + (-3)}{2}, \frac{1 + 6}{2} \right) = \left( \frac{6}{2}, \frac{7}{2} \right) = (3, 3.5) \]
Thus, the midpoint of the segment is \((3, 3.5)\).
Final answers:
- Distance: \(13.0\)
- Midpoint: \((3, 3.5)\)
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