Question

find the distance between (-8,-3) and (-2, -5) round your answer to the nearest hundreth if nessacary

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, substituting in the values:

\[
d = \sqrt{((-2) - (-8))^2 + ((-5) - (-3))^2}
\]
\[
= \sqrt{(-2 + 8)^2 + (-5 + 3)^2}
\]
\[
= \sqrt{(6)^2 + (-2)^2}
\]
\[
= \sqrt{36 + 4}
\]
\[
= \sqrt{40}
\]
\[
= \sqrt{4 \times 10}
\]
\[
= 2\sqrt{10}
\]

Now, we can find the decimal value of \(2\sqrt{10}\):

\[
\sqrt{10} \approx 3.1623
\]

Thus,

\[
2\sqrt{10} \approx 2 \times 3.1623 \approx 6.3246
\]

Rounding to the nearest hundredth, the distance is:

\[
\boxed{6.32}
\]