To find the distance between the two points \((-2, -1)\) and \((2, 4)\), we can apply the Pythagorean Theorem. The distance formula is derived from the Pythagorean Theorem and is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. For the points provided:
- \((x_1, y_1) = (-2, -1)\)
- \((x_2, y_2) = (2, 4)\)
Now, we can substitute these values into the distance formula:
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Calculate \(x_2 - x_1\): \[ 2 - (-2) = 2 + 2 = 4 \]
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Calculate \(y_2 - y_1\): \[ 4 - (-1) = 4 + 1 = 5 \]
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Substitute these results into the distance formula: \[ d = \sqrt{(4)^2 + (5)^2} = \sqrt{16 + 25} = \sqrt{41} \]
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Now, round \(\sqrt{41}\) to the nearest hundredth: \[ \sqrt{41} \approx 6.403124237 \approx 6.40 , (\text{to the nearest hundredth}) \]
Thus, the length between the two points is approximately 6.40. Therefore, the correct answer is:
6.40