To find the distance between the two points \( A(2, -3) \) and \( B(5, 5) \), we can use the Pythagorean Theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Plugging in the coordinates of points A and B:
- \( (x_1, y_1) = (2, -3) \)
- \( (x_2, y_2) = (5, 5) \)
Calculating the differences:
\[ x_2 - x_1 = 5 - 2 = 3 \] \[ y_2 - y_1 = 5 - (-3) = 5 + 3 = 8 \]
Now, substitute these values into the distance formula:
\[ d = \sqrt{(3)^2 + (8)^2} \] \[ d = \sqrt{9 + 64} \] \[ d = \sqrt{73} \]
Calculating the square root of 73:
\[ \sqrt{73} \approx 8.54 \]
Rounding to the nearest hundredth, the distance between the two points is approximately \( 8.54 \).
The answer is:
8.54