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, which is given by:

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

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

Substituting the coordinates into the formula, we have:

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

Calculating the differences:

\[
x_2 - x_1 = -2 + 8 = 6
\]
\[
y_2 - y_1 = -5 + 3 = -2
\]

Now substituting these differences back into the formula:

\[
d = \sqrt{(6)^2 + (-2)^2}
\]
\[
d = \sqrt{36 + 4}
\]
\[
d = \sqrt{40}
\]

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

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

Next, we can calculate the numerical value of \(2\sqrt{10}\):

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

Therefore:

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

Rounding to the nearest hundredth, the distance is:

\[
\boxed{6.32}
\]