Question

Find the distance between (−8, −3)
and (−2, −5)
. Round your answer to the nearest hundredth, if necessary.(1 point)

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, substituting the values into the formula:

\[
d = \sqrt{((-2) - (-8))^2 + ((-5) - (-3))^2}
\]

Calculating each part:

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

Now substituting these results back into the distance formula:

\[
d = \sqrt{(6)^2 + (-2)^2}
\]

Calculating the squares:

\[
d = \sqrt{36 + 4} = \sqrt{40}
\]

Now we can simplify \(\sqrt{40}\):

\[
\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
\]

Next, we can approximate \(\sqrt{10}\):

\(\sqrt{10} \approx 3.162\)

So,

\[
d \approx 2 \times 3.162 = 6.324
\]

Finally, rounding to the nearest hundredth:

\[
d \approx 6.32
\]

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