Question

Question Find the distance between (−8, −3) and (−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:

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

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

Now we plug in the values:

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

Calculating each part:

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

Now we can use these values in the distance formula:

\[
d = \sqrt{(6)^2 + (-2)^2}
\]
\[
d = \sqrt{36 + 4}
\]
\[
d = \sqrt{40}
\]
\[
d \approx 6.32455532
\]

Rounding to the nearest hundredth:

\[
d \approx 6.32
\]

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