To find the distance between the two 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 \((x_2, y_2) = (-3, 6)\).
Plugging in the values:
\[ d = \sqrt{((-3) - 9)^2 + (6 - 1)^2} \] \[ d = \sqrt{(-12)^2 + (5)^2} \] \[ d = \sqrt{144 + 25} \] \[ d = \sqrt{169} \] \[ d = 13 \]
So the distance between the points is 13.0 units.
Next, we find the midpoint of the segment connecting the two points. The midpoint formula is given by:
\[ M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
Calculating the midpoint for the points (9, 1) and (-3, 6):
\[ M = \left(\frac{9 + (-3)}{2}, \frac{1 + 6}{2}\right) \] \[ M = \left(\frac{6}{2}, \frac{7}{2}\right) \] \[ M = (3, 3.5) \]
Therefore, the midpoint is (3, 3.5).