Question

The coordinates of a line segmant QR are Q(8,2_ and R(5,7) which measurement is closest to the length of the line segment?
5
3.9
5.8
4

Answer 1

To find the length of the line segment QR with endpoints Q(8, 2) and R(5, 7), we 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 \( (x_2, y_2) = (5, 7) \).

1. Calculate \( x_2 - x_1 \):
\[
5 - 8 = -3
\]

2. Calculate \( y_2 - y_1 \):
\[
7 - 2 = 5
\]

3. Substitute into the distance formula:
\[
d = \sqrt{(-3)^2 + (5)^2}
\]
\[
d = \sqrt{9 + 25}
\]
\[
d = \sqrt{34}
\]

4. To approximate \( \sqrt{34} \), we can calculate it:
- \( 5.8^2 = 33.64 \) which is close to 34,
- \( 5.9^2 = 34.81 \) which is a little higher than 34.

Thus, \( \sqrt{34} \) is approximately \( 5.83 \).

From the given options, the closest measurement to the length of the line segment QR is **5.8**.