Question

A (2,4)
B(-2,-1)

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

(1 point)

9

41

5.57

6:40

Answer 1

To find the distance between the points \( A(2, 4) \) and \( B(-2, -1) \), 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.

Substituting in the values:

- \( x_1 = 2 \)
- \( y_1 = 4 \)
- \( x_2 = -2 \)
- \( y_2 = -1 \)

Now, plug these into the formula:

\[
d = \sqrt{((-2) - 2)^2 + ((-1) - 4)^2}
\]
\[
d = \sqrt{(-4)^2 + (-5)^2}
\]
\[
d = \sqrt{16 + 25}
\]
\[
d = \sqrt{41}
\]

Now we can find the value of \( \sqrt{41} \):

\[
\sqrt{41} \approx 6.4
\]

Rounding to the nearest hundredth, the final answer is:

\[
\boxed{6.40}
\]