Question

Find the distance between the points (0, -6) and (-2, -5)
Write your answer as a whole number or a fully simplified radical expression. Do not round.

Answer 1

To find the distance between the points \((0, -6)\) and \((-2, -5)\), we can use the distance formula:

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

Here, we can assign:
- \((x_1, y_1) = (0, -6)\)
- \((x_2, y_2) = (-2, -5)\)

Now, we can calculate each component of the distance formula:

1. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = -2 - 0 = -2
\]

2. Calculate \(y_2 - y_1\):
\[
y_2 - y_1 = -5 - (-6) = -5 + 6 = 1
\]

Now substitute these values into the distance formula:

\[
d = \sqrt{(-2)^2 + (1)^2}
\]

Calculating the squares:

\[
(-2)^2 = 4 \quad \text{and} \quad (1)^2 = 1
\]

So now, we have:

\[
d = \sqrt{4 + 1} = \sqrt{5}
\]

Thus, the distance between the points \((0, -6)\) and \((-2, -5)\) is:

\[
\boxed{\sqrt{5}}
\]