Question

Whenever he visits Lowell, Levi has to drive 7.5 miles due north from home. Whenever he visits Westminster, he has to drive 5 miles due east from home. How far apart are Lowell and Westminster, measured in a straight line? If necessary, round to the nearest tenth.

miles

Answer 1

To find the straight-line distance between Lowell and Westminster, we can use the Pythagorean theorem. In this case, Levi's home can be considered as the origin point (0,0) on a coordinate plane.

- The coordinates of Lowell, which is 7.5 miles due north, would be (0, 7.5).
- The coordinates of Westminster, which is 5 miles due east, would be (5, 0).

We can determine the distance \(d\) between these two points using the Pythagorean theorem:

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

Substituting the coordinates of Lowell \((x_1, y_1) = (0, 7.5)\) and Westminster \((x_2, y_2) = (5, 0)\):

\[
d = \sqrt{(5 - 0)^2 + (0 - 7.5)^2}
\]
\[
= \sqrt{(5)^2 + (-7.5)^2}
\]
\[
= \sqrt{25 + 56.25}
\]
\[
= \sqrt{81.25}
\]
\[
\approx 9.01
\]

Rounding to the nearest tenth, the straight-line distance between Lowell and Westminster is approximately:

\[
\boxed{9.0} \text{ miles}
\]