Question

Find the distance between (5,5) and (2,-3) round your answer to the nearest hundredth if necessary

Answer 1

To find the distance between the two points \((5, 5)\) and \((2, -3)\), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1) = (5, 5)\) and \((x_2, y_2) = (2, -3)\).

Plugging in the values:

\[
d = \sqrt{(2 - 5)^2 + (-3 - 5)^2}
\]
\[
= \sqrt{(-3)^2 + (-8)^2}
\]
\[
= \sqrt{9 + 64}
\]
\[
= \sqrt{73}
\]

Calculating \(\sqrt{73}\):

\(\sqrt{73} \approx 8.544\)

Rounding to the nearest hundredth, the distance is approximately:

\[
\boxed{8.54}
\]