Question

Emaniee would like to build a ramp for her dog over some stairs. Compute the distance between points B and D
B (-2, -6)
D (5, 11)

Answer 1

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:

\[
\boxed{13\sqrt{2}}
\]