Question

Find the distance and round to the nearest hundredth
(13,-16) (-9,-5)

Answer 1

To find the distance between the points \((13, -16)\) and \((-9, -5)\), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Where \((x_1, y_1) = (13, -16)\) and \((x_2, y_2) = (-9, -5)\).

Now, substituting the values into the formula:

1. Calculate \(x_2 - x_1\):
\[
-9 - 13 = -22
\]

2. Calculate \(y_2 - y_1\):
\[
-5 - (-16) = -5 + 16 = 11
\]

3. Now substitute these results back into the distance formula:
\[
d = \sqrt{(-22)^2 + (11)^2}
\]

4. Calculate \((-22)^2\) and \(11^2\):
\[
(-22)^2 = 484
\]
\[
(11)^2 = 121
\]

5. Add these two results:
\[
484 + 121 = 605
\]

6. Take the square root:
\[
d = \sqrt{605} \approx 24.586
\]

Finally, rounding to the nearest hundredth, we get:
\[
\boxed{24.59}
\]