To compute the distance between points B (-2, -6) and D (5, 11), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \((x_1, y_1)\) are the coordinates of point B, and \((x_2, y_2)\) are the coordinates of point D.
Here, we have:
- \(x_1 = -2\)
- \(y_1 = -6\)
- \(x_2 = 5\)
- \(y_2 = 11\)
Now substituting these values into the distance formula:
\[ d = \sqrt{(5 - (-2))^2 + (11 - (-6))^2} \]
Simplifying inside the parentheses:
\[ d = \sqrt{(5 + 2)^2 + (11 + 6)^2} \] \[ d = \sqrt{(7)^2 + (17)^2} \] \[ d = \sqrt{49 + 289} \] \[ d = \sqrt{338} \]
Now we can simplify \( \sqrt{338} \):
The prime factorization of 338 is \(2 \times 169\). Since \(169\) is a perfect square (\(13^2\)), we can simplify further:
\[ \sqrt{338} = \sqrt{2 \times 13^2} = 13\sqrt{2} \]
So, the distance between points B and D is:
\[ \text{Distance} = 13\sqrt{2} \approx 18.38 \]
Thus, the final answer is:
\[ \boxed{13\sqrt{2}} \]
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