To find the length between the two points \((-2, -1)\) and \((2, 4)\) using the Pythagorean Theorem, we first calculate the difference in the x-coordinates and the difference in the y-coordinates.
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Calculate the difference in the x-coordinates:
\[ x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \]
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Calculate the difference in the y-coordinates:
\[ y_2 - y_1 = 4 - (-1) = 4 + 1 = 5 \]
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Use the Pythagorean theorem:
The distance \(d\) between the points is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Plugging in the differences:
\[ d = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} \]
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Approximate \(\sqrt{41}\):
Using a calculator,
\[ \sqrt{41} \approx 6.403 \]
Rounding to the nearest hundredth, we get:
\[ d \approx 6.40 \]
The answer is 6.40.