To find the distance between two points \( J = (-9, 9) \) and \( E = (-2, 1) \) in the coordinate plane, we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) = (-9, 9) \) and \( (x_2, y_2) = (-2, 1) \).
Now, we will calculate the differences:
\[ x_2 - x_1 = -2 - (-9) = -2 + 9 = 7 \] \[ y_2 - y_1 = 1 - 9 = -8 \]
Now we can plug these values into the distance formula:
\[ d = \sqrt{(7)^2 + (-8)^2} \]
Calculating the squares:
\[ d = \sqrt{49 + 64} \] \[ d = \sqrt{113} \]
Thus, the exact distance between points \( J \) and \( E \) is
\[ \boxed{\sqrt{113}}. \]