Question

Find the distance between (−8, −3) and (−2, −5) . Round your answer to the nearest hundredth, if necessary.

Answer 1

To find the distance between the points \((-8, -3)\) and \((-2, -5)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-8, -3)\) and \((x_2, y_2) = (-2, -5)\).

Now, substitute the values into the formula:

1. Calculate the differences:
- \(x_2 - x_1 = -2 - (-8) = -2 + 8 = 6\)
- \(y_2 - y_1 = -5 - (-3) = -5 + 3 = -2\)

2. Now substitute these values into the formula:
\[
d = \sqrt{(6)^2 + (-2)^2}
\]

3. Calculate the squares:
\[
d = \sqrt{36 + 4}
\]

4. Adding those:
\[
d = \sqrt{40}
\]

5. Now simplify \(\sqrt{40}\):
\[
d = \sqrt{4 \times 10} = 2\sqrt{10}
\]

6. Now, let's calculate this value. The approximate value of \(\sqrt{10}\) is about \(3.1623\), so:
\[
d \approx 2 \times 3.1623 \approx 6.3246
\]

Rounding this to the nearest hundredth, we get:
\[
d \approx 6.32
\]

Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately \(6.32\).