To find the distance between the two points \( A(2, -3) \) and \( B(5, 5) \), we can use the distance formula derived from the Pythagorean Theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For points \( A(2, -3) \) and \( B(5, 5) \):
- \( x_1 = 2 \)
- \( y_1 = -3 \)
- \( x_2 = 5 \)
- \( y_2 = 5 \)
Now substitute these values into the distance formula:
\[ d = \sqrt{(5 - 2)^2 + (5 - (-3))^2} \] \[ d = \sqrt{(3)^2 + (5 + 3)^2} \] \[ d = \sqrt{9 + 8^2} \] \[ d = \sqrt{9 + 64} \] \[ d = \sqrt{73} \]
Now we calculate \( \sqrt{73} \):
\[ \sqrt{73} \approx 8.544 \]
Rounded to the nearest hundredth, this is approximately \( 8.54 \).
Thus, the distance between points A and B is \( \boxed{8.54} \).