Question

Find the distance between (-8, -3) and (-2, -5). Round your answer to the nearest hundreth

Answer 1

To find the distance between the 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 coordinates into the formula:

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

Calculating each part:

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 values back into the formula:

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

Calculating the squares:

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

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

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

To evaluate \(2\sqrt{10}\), we can find \(\sqrt{10} \approx 3.1623\):

\[
d \approx 2 \times 3.1623 \approx 6.3246
\]

Rounding to the nearest hundredth:

\[
d \approx 6.32
\]

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