To find the distance between the points \((3, -5)\) and \((-2, -7)\) on the coordinate plane, we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (3, -5)\) and \((x_2, y_2) = (-2, -7)\).
Now, substitute these values into the formula:
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Calculate \(x_2 - x_1\): \[ x_2 - x_1 = -2 - 3 = -5 \]
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Calculate \(y_2 - y_1\): \[ y_2 - y_1 = -7 - (-5) = -7 + 5 = -2 \]
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Now plug these values into the distance formula: \[ d = \sqrt{(-5)^2 + (-2)^2} \]
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Calculate \((-5)^2\) and \((-2)^2\): \[ (-5)^2 = 25 \quad \text{and} \quad (-2)^2 = 4 \]
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Add these results: \[ 25 + 4 = 29 \]
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Finally, take the square root: \[ d = \sqrt{29} \]
Next, we approximate \(\sqrt{29}\). The square root of 29 falls between the perfect squares of 25 and 36:
\[ 5^2 = 25 \quad \text{and} \quad 6^2 = 36 \]
Calculating a more precise value, we find:
\[ \sqrt{29} \approx 5.385 \]
Rounding this to the nearest tenth, we get:
\[ \sqrt{29} \approx 5.4 \]
Thus, the distance between the points \((3, -5)\) and \((-2, -7)\) rounded up to the nearest tenth of a unit is:
\[ \boxed{5.4} \]
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