To find the distance between the points \((-8, -2)\) and \( (0, -5)\), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, we have:
- \( (x_1, y_1) = (-8, -2) \)
- \( (x_2, y_2) = (0, -5) \)
Now, we will substitute these values into the distance formula:
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Calculate \( x_2 - x_1 \): \[ x_2 - x_1 = 0 - (-8) = 0 + 8 = 8 \]
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Calculate \( y_2 - y_1 \): \[ y_2 - y_1 = -5 - (-2) = -5 + 2 = -3 \]
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Now substituting into the distance formula: \[ d = \sqrt{(8)^2 + (-3)^2} \]
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Calculate \( (8)^2 \) and \( (-3)^2 \): \[ (8)^2 = 64 \] \[ (-3)^2 = 9 \]
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Now, adding these results together: \[ d = \sqrt{64 + 9} = \sqrt{73} \]
Thus, the distance between the points \((-8, -2)\) and \( (0, -5)\) is:
\[ \sqrt{73} \text{ units.} \]
This is the fully simplified radical expression for the distance.