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.
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