To find the distance between the points \( (3, -5) \) and \( (-2, -7) \), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we have:
- \( (x_1, y_1) = (3, -5) \)
- \( (x_2, y_2) = (-2, -7) \)
Now, substituting the coordinates into the distance formula:
\[ d = \sqrt{((-2) - 3)^2 + ((-7) - (-5))^2} \]
This simplifies to:
\[ d = \sqrt{(-5)^2 + (-2)^2} \]
Calculating each term:
\[ (-5)^2 = 25, \quad (-2)^2 = 4 \]
Now add these values:
\[ d = \sqrt{25 + 4} = \sqrt{29} \]
Next, we calculate \( \sqrt{29} \). The approximate value is:
\[ \sqrt{29} \approx 5.385 \]
Finally, rounding \( 5.385 \) up to the nearest tenth:
\[ \text{Rounded distance} \approx 5.4 \]
Therefore, the distance between the two points, rounded to the nearest tenth, is
\[ \boxed{5.4} \]
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