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 \( (x_2, y_2) = (5, 7) \).
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Calculate \( x_2 - x_1 \): \[ 5 - 8 = -3 \]
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Calculate \( y_2 - y_1 \): \[ 7 - 2 = 5 \]
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Substitute into the distance formula: \[ d = \sqrt{(-3)^2 + (5)^2} \] \[ d = \sqrt{9 + 25} \] \[ d = \sqrt{34} \]
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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.
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