Question

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

−
3
)
and (−2, −5)
(
−
2
,

−
5
)
. Round your answer to the nearest hundredth, if necessary.

Answer 1

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

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

Here, the coordinates of the first point \((x_1, y_1)\) are \((-8, -3)\) and the coordinates of the second point \((x_2, y_2)\) are \((-2, -5)\).

Now substitute the values into the distance formula:

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

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

3. Now substitute these values into the distance formula:
\[
d = \sqrt{(6)^2 + (-2)^2} = \sqrt{36 + 4} = \sqrt{40}
\]

4. Simplifying \(\sqrt{40}\):
\[
\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
\]

5. Now, calculate the numerical approximation of \(2\sqrt{10}\):
\[
2\sqrt{10} \approx 2 \times 3.1623 \approx 6.3246
\]

Rounding this to the nearest hundredth gives:

\[
\text{Distance} \approx 6.32
\]

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