To find the distance between the points \( C = (2, -1) \) and \( N = (7, -7) \) in the coordinate plane, we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points. In this case, we have:
- \( (x_1, y_1) = (2, -1) \)
- \( (x_2, y_2) = (7, -7) \)
Now applying the distance formula:
\[ d = \sqrt{(7 - 2)^2 + (-7 - (-1))^2} \]
Calculating the differences:
\[ d = \sqrt{(5)^2 + (-7 + 1)^2} \] \[ d = \sqrt{(5)^2 + (-6)^2} \]
Calculating the squares:
\[ d = \sqrt{25 + 36} \] \[ d = \sqrt{61} \]
Thus, the exact distance between the points \( C \) and \( N \) is
\[ \boxed{\sqrt{61}}. \]
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