Question

Find the distance between the points (
–
10,
–
7) and (
–
2,
–
9).
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 \((-10, -7)\) and \((-2, -9)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-10, -7)\) and \((x_2, y_2) = (-2, -9)\).

Now, let's calculate the differences:

\[
x_2 - x_1 = -2 - (-10) = -2 + 10 = 8
\]
\[
y_2 - y_1 = -9 - (-7) = -9 + 7 = -2
\]

Next, we substitute these values into the distance formula:

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

Calculating the squares:

\[
d = \sqrt{64 + 4}
\]
\[
d = \sqrt{68}
\]

Now we can simplify \(\sqrt{68}\):

\[
\sqrt{68} = \sqrt{4 \times 17} = \sqrt{4} \cdot \sqrt{17} = 2\sqrt{17}
\]

Therefore, the distance between the points \((-10, -7)\) and \((-2, -9)\) is

\[
\boxed{2\sqrt{17}} \text{ units}
\]