Question

Find the distance between (−8, −3)
(
−
8
,

−
3
)
and (−2, −5)
(
−
2
,

−
5
)
. Round your answer to the nearest hundredth, if necessary.(1 point)
units

Answer 1

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

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

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

Now plug in the values:

1. Calculate \(x_2 - x_1\):
\[
-2 - (-8) = -2 + 8 = 6
\]

2. Calculate \(y_2 - y_1\):
\[
-5 - (-3) = -5 + 3 = -2
\]

Now substitute these into the distance formula:

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

Calculating the squares:

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

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

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

Now we calculate \(2\sqrt{10}\) using the approximate value of \(\sqrt{10} \approx 3.162\):

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

Rounding to the nearest hundredth, we get:

\[
\boxed{6.32} \text{ units}
\]