To find the distance between two points \( A(2, -3) \) and \( B(5, 5) \), we can use the distance formula, which is derived from the Pythagorean theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \):
- \( x_1 = 2 \), \( y_1 = -3 \)
- \( x_2 = 5 \), \( y_2 = 5 \)
Now, plug the coordinates into the distance formula:
\[ d = \sqrt{(5 - 2)^2 + (5 - (-3))^2} \] \[ d = \sqrt{(3)^2 + (5 + 3)^2} \] \[ d = \sqrt{9 + 64} \] \[ d = \sqrt{73} \]
Now, calculate \( \sqrt{73} \):
\[ \sqrt{73} \approx 8.54 \]
Thus, the length between points A and B is approximately 8.54, rounded to the nearest hundredth.
The correct answer is:
8.54