To calculate the distance between the points \( C(3, -8) \) and \( E(7, -1) \) in the coordinate plane, we use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) = (3, -8) \) and \( (x_2, y_2) = (7, -1) \).
- Calculate \( x_2 - x_1 \):
\[ x_2 - x_1 = 7 - 3 = 4 \]
- Calculate \( y_2 - y_1 \):
\[ y_2 - y_1 = -1 - (-8) = -1 + 8 = 7 \]
- Now substitute these values back into the distance formula:
\[ d = \sqrt{(4)^2 + (7)^2} \]
- Calculate the squares:
\[ 4^2 = 16 \quad \text{and} \quad 7^2 = 49 \]
- Add the squares:
\[ 16 + 49 = 65 \]
- Take the square root:
\[ d = \sqrt{65} \]
Thus, the exact distance between the points \( C \) and \( E \) is
\[ \sqrt{65} \]