Question

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

(−5, −1), (7, −8)

Question 3 options:

4.4


9.2


12.6


13.9

Answer 1

To find the distance between the points \((-5, -1)\) and \((7, -8)\), we can use the distance formula:

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

where \((x_1, y_1)\) are the coordinates of the first point, and \((x_2, y_2)\) are the coordinates of the second point.

Plugging in the coordinates:

- \((x_1, y_1) = (-5, -1)\)
- \((x_2, y_2) = (7, -8)\)

Now substitute into the formula:

\[
d = \sqrt{(7 - (-5))^2 + (-8 - (-1))^2}
\]

Calculating the differences:

\[
7 - (-5) = 7 + 5 = 12
\]
\[
-8 - (-1) = -8 + 1 = -7
\]

Now substitute these back into the distance formula:

\[
d = \sqrt{(12)^2 + (-7)^2}
\]
\[
d = \sqrt{144 + 49}
\]
\[
d = \sqrt{193}
\]

Now, we need to calculate \(\sqrt{193}\):

\[
\sqrt{193} \approx 13.9
\]

Thus, the distance between the points \((-5, -1)\) and \((7, -8)\) is approximately **13.9**.

So the answer is:

**13.9**