Question

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

(−1, 7), (−8, 6)

Question 4 options:

2.8


4.7


7.1


5.8

Answer 1

To find the distance between the points \((-1, 7)\) and \((-8, 6)\), we can use the distance formula, which is given by:

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

In this case, we have:
- \( (x_1, y_1) = (-1, 7) \)
- \( (x_2, y_2) = (-8, 6) \)

Now substitute the coordinates into the distance formula:

\[
d = \sqrt{((-8) - (-1))^2 + (6 - 7)^2}
\]
\[
= \sqrt{(-8 + 1)^2 + (-1)^2}
\]
\[
= \sqrt{(-7)^2 + (-1)^2}
\]
\[
= \sqrt{49 + 1}
\]
\[
= \sqrt{50}
\]
\[
= \sqrt{25 \times 2}
\]
\[
= 5\sqrt{2}
\]

Calculating \(5\sqrt{2}\) using the approximate value of \(\sqrt{2} \approx 1.414\):

\[
5 \times 1.414 \approx 7.07
\]

Rounding \(7.07\) to the nearest tenth gives us approximately \(7.1\).

Therefore, the distance between the points \((-1, 7)\) and \((-8, 6)\) is:

\[
\boxed{7.1}
\]