To find the length between the two points A(2, -3) and B(5, 5), we can use the distance formula, which is derived from the Pythagorean Theorem. The formula for the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For the given points A(2, -3) and B(5, 5):
- \(x_1 = 2\), \(y_1 = -3\)
- \(x_2 = 5\), \(y_2 = 5\)
Now, plug in the coordinates:
\[ d = \sqrt{(5 - 2)^2 + (5 - (-3))^2} \] \[ d = \sqrt{(3)^2 + (5 + 3)^2} \] \[ d = \sqrt{3^2 + 8^2} \] \[ d = \sqrt{9 + 64} \] \[ d = \sqrt{73} \]
Now, we can calculate the numerical value of \(\sqrt{73}\):
\[ \sqrt{73} \approx 8.54 \]
So, the length between the two points, rounded to the nearest hundredth, is approximately \(8.54\).
The correct response is:
8.54