Question

A coordinate plane is placed over the map of a town. A library is located at ( – 5, 1), and a
museum is located at (3,5). What is the distance, to the nearest tenth, from the library to the
museum?

Answers

GPT-4o mini
To find the distance between the library located at the point \((-5, 1)\) and the museum located at the point \((3, 5)\), we can use the distance formula, which is given by:

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

In this case, the coordinates are:
- \( (x_1, y_1) = (-5, 1) \)
- \( (x_2, y_2) = (3, 5) \)

Plugging in the coordinates into the distance formula:

\[
d = \sqrt{(3 - (-5))^2 + (5 - 1)^2}
\]
\[
= \sqrt{(3 + 5)^2 + (5 - 1)^2}
\]
\[
= \sqrt{(8)^2 + (4)^2}
\]
\[
= \sqrt{64 + 16}
\]
\[
= \sqrt{80}
\]
\[
= \sqrt{16 \cdot 5}
\]
\[
= 4\sqrt{5}
\]

To find \(4\sqrt{5}\) to the nearest tenth, we can approximate \(\sqrt{5}\). The value of \(\sqrt{5} \approx 2.236\), so:

\[
4\sqrt{5} \approx 4 \cdot 2.236 \approx 8.944
\]

Rounding \(8.944\) to the nearest tenth gives us:

\[
\boxed{8.9}
\]

Thus, the distance from the library to the museum is approximately \(8.9\) units.

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