Question

The coordinates of line segment QR are Q(8,2) and R(5,7) .

Which measurement is closest to the length of line segment QR in units?

(1 point)
Responses

5
5

3.9
3.9

5.8
5.8

4

Answer 1

To find the length of line segment QR with endpoints Q(8, 2) and R(5, 7), you can use the distance formula:

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

Here, \( (x_1, y_1) = (8, 2) \) and \( (x_2, y_2) = (5, 7) \).

Now, plug in the coordinates into the formula:

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

Calculating inside the square root:

\[
d = \sqrt{(-3)^2 + (5)^2}
\]
\[
d = \sqrt{9 + 25}
\]
\[
d = \sqrt{34}
\]

Now calculate \(\sqrt{34}\):

\[
\sqrt{34} \approx 5.83
\]

So the length of line segment QR is approximately 5.8 units.

The closest measurement from the options provided is:

**5.8**.