Question

Whenever she visits Morristown, Shelley has to drive 8 miles due north from home. Whenever she visits Cedarburg, she has to drive 15 miles due east from home. How far apart are Morristown and Cedarburg, measured in a straight line? miles

Answer 1

To find the straight-line distance between Morristown and Cedarburg, we can use the Pythagorean theorem, as their positions can be represented in a coordinate system.

Let’s define:

- Morristown is located 8 miles north of Shelley's home, which we can represent as the point \( (0, 8) \).
- Cedarburg is located 15 miles east of her home, which we can represent as the point \( (15, 0) \).

Now, we can determine the distance \( d \) between the points \( (0, 8) \) and \( (15, 0) \) using the distance formula:

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

Where:
- \( (x_1, y_1) = (0, 8) \)
- \( (x_2, y_2) = (15, 0) \)

Plugging in the coordinates:

\[
d = \sqrt{(15 - 0)^2 + (0 - 8)^2}
\]
\[
d = \sqrt{15^2 + (-8)^2}
\]
\[
d = \sqrt{225 + 64}
\]
\[
d = \sqrt{289}
\]
\[
d = 17
\]

Thus, the distance between Morristown and Cedarburg is \( \boxed{17} \) miles.