Question

A (2,-3)
B (5,5)

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.

(1 point)

8.54

73

7.62

11

Answer 1

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**