To find the distance between the two points \((-5, 5)\) and \((2, -2)\) using the Pythagorean Theorem, we can follow these steps:
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Identify the coordinates:
- Point 1: \((x_1, y_1) = (-5, 5)\)
- Point 2: \((x_2, y_2) = (2, -2)\)
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Calculate the differences in the x and y coordinates: \[ \Delta x = x_2 - x_1 = 2 - (-5) = 2 + 5 = 7 \] \[ \Delta y = y_2 - y_1 = -2 - 5 = -7 \]
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Use the Pythagorean Theorem to find the distance \(d\): \[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} \]
Plugging in the values: \[ d = \sqrt{(7)^2 + (-7)^2} = \sqrt{49 + 49} = \sqrt{98} \]
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Calculate \(\sqrt{98}\) and round to the nearest tenth: \[ \sqrt{98} \approx 9.899 \]
Rounding to the nearest tenth, we get: \[ d \approx 9.9 \]
Therefore, the distance between the two points is approximately 9.9.