To find the distance between the points \((0, 2)\) and \((-9, 3)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (-9, 3)\). Plugging in the coordinates:
\[ d = \sqrt{((-9) - (0))^2 + (3 - 2)^2} \]
This simplifies to:
\[ d = \sqrt{(-9)^2 + (1)^2} \] \[ d = \sqrt{81 + 1} \] \[ d = \sqrt{82} \]
The distance between the points \((0, 2)\) and \((-9, 3)\) is:
\[ \sqrt{82} \text{ units} \]
This is the fully simplified radical expression.