To find the distance between the points \((0.6, 3.2)\) and \((3.2, -0.6)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Given the points:
- \( (x_1, y_1) = (0.6, 3.2) \)
- \( (x_2, y_2) = (3.2, -0.6) \)
We compute the differences:
- \( x_2 - x_1 = 3.2 - 0.6 = 2.6 \)
- \( y_2 - y_1 = -0.6 - 3.2 = -3.8 \)
Now we square these differences:
- \( (x_2 - x_1)^2 = (2.6)^2 = 6.76 \)
- \( (y_2 - y_1)^2 = (-3.8)^2 = 14.44 \)
Now we can plug these values into the distance formula:
\[ d = \sqrt{6.76 + 14.44} = \sqrt{21.20} \]
Calculating the square root:
\[ d \approx 4.605 \]
Rounding this to three decimal places, we get:
\[ d \approx 4.605 \]
Thus, the approximate distance between the points \((0.6, 3.2)\) and \((3.2, -0.6)\) is \(\boxed{4.605}\).
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