To find the distance from first base at the point (4, 0) to home at (0, -4), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this scenario, we have:
- \( (x_1, y_1) = (4, 0) \) (coordinates of first base)
- \( (x_2, y_2) = (0, -4) \) (coordinates of home)
Plugging in these values into the distance formula:
\[ d = \sqrt{(0 - 4)^2 + (-4 - 0)^2} \]
Calculating the differences:
\[ d = \sqrt{(-4)^2 + (-4)^2} \]
Squaring the terms:
\[ d = \sqrt{16 + 16} \]
Adding them together:
\[ d = \sqrt{32} \]
This can be simplified further:
\[ d = \sqrt{16 \times 2} = 4\sqrt{2} \]
To provide an approximate decimal value for the distance, we can calculate \( \sqrt{2} \) which is approximately 1.414. Thus:
\[ d \approx 4 \times 1.414 = 5.656 \]
Therefore, the shortest approximate unit distance from first base to home is:
\[ \boxed{5.656} \]
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