Question

Find the distance between the points (
–
8,
–
2) and (0,
–
6).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units

Answer 1

To find the distance between the points \((-8, -2)\) and \((0, -6)\), we can use the distance formula:

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

Where \((x_1, y_1) = (-8, -2)\) and \((x_2, y_2) = (0, -6)\).

Now, we can substitute the coordinates into the formula:

1. Calculate \(x_2 - x_1\) and \(y_2 - y_1\):

\[
x_2 - x_1 = 0 - (-8) = 0 + 8 = 8
\]
\[
y_2 - y_1 = -6 - (-2) = -6 + 2 = -4
\]

2. Now, plug these values into the distance formula:

\[
d = \sqrt{(8)^2 + (-4)^2}
\]

3. Calculate \((8)^2\) and \((-4)^2\):

\[
(8)^2 = 64
\]
\[
(-4)^2 = 16
\]

4. Now, add these two results:

\[
d = \sqrt{64 + 16} = \sqrt{80}
\]

5. Finally, simplify \(\sqrt{80}\):

\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
\]

Thus, the distance between the points \((-8, -2)\) and \((0, -6)\) is

\[
\boxed{4\sqrt{5}} \text{ units.}
\]