To find the distance between the points A (2, -3) and B (5, 5) using the Pythagorean Theorem, you can use the distance formula, which is derived from the 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 the points A (2, -3) and B (5, 5):
- \(x_1 = 2\), \(y_1 = -3\)
- \(x_2 = 5\), \(y_2 = 5\)
Now, plug in the values:
\[ d = \sqrt{(5 - 2)^2 + (5 - (-3))^2} \] \[ d = \sqrt{(3)^2 + (8)^2} \] \[ d = \sqrt{9 + 64} \] \[ d = \sqrt{73} \]
Now calculate \(\sqrt{73}\):
\[ d \approx 8.54 \]
So, the length between the two points A and B is approximately 8.54.
The correct answer is 8.54.