Question

What is the unit distance, rounded to the nearest hundredth, between the points negative 5 comma 2 and 3 comma 7? Enter the answer in the box.

Response area with 1 text input box
units

Answer 1

To find the distance between the points \((-5, 2)\) and \((3, 7)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (-5, 2)\) and \((x_2, y_2) = (3, 7)\).

Now we will plug in the values:

\[
d = \sqrt{(3 - (-5))^2 + (7 - 2)^2}
\]
\[
= \sqrt{(3 + 5)^2 + (7 - 2)^2}
\]
\[
= \sqrt{(8)^2 + (5)^2}
\]
\[
= \sqrt{64 + 25}
\]
\[
= \sqrt{89}
\]

Now, we can calculate \(\sqrt{89}\):

\(\sqrt{89} \approx 9.434\)

Rounding to the nearest hundredth, we get:

**9.43**

Therefore, the unit distance between the points, rounded to the nearest hundredth, is:

9.43 units