To find the distance between the points \( (6,1) \) and \( (-9,6) \), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) = (6, 1) \) and \( (x_2, y_2) = (-9, 6) \).
Substituting the values into the formula:
\[ d = \sqrt{((-9) - 6)^2 + (6 - 1)^2} \] \[ = \sqrt{(-15)^2 + (5)^2} \] \[ = \sqrt{225 + 25} \] \[ = \sqrt{250} \] \[ = \sqrt{25 \times 10} \] \[ = 5\sqrt{10} \]
Next, we calculate \( 5\sqrt{10} \). Using an approximate value for \( \sqrt{10} \approx 3.162 \):
\[ 5\sqrt{10} \approx 5 \times 3.162 \approx 15.81 \]
Rounding this to the nearest tenth gives us approximately \( 15.8 \) units.
Thus, the distance between the two points, rounded to the nearest tenth of a unit, is:
15.8 units