Question

On a map’s coordinate grid, Walt City is located at ( – 1, – 3) and Koshville is located at (4,9).
How long is a train’s route as the train travels along a straight line from Walt City to Koshville? (One
map unit equals one mile)

Answer 1

To find the distance between two points on a coordinate grid, you can use the distance formula:

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

In this case, the coordinates for Walt City are \((-1, -3)\) and for Koshville are \((4, 9)\). Let's assign:

- \((x_1, y_1) = (-1, -3)\)
- \((x_2, y_2) = (4, 9)\)

Now we can plug these values into the distance formula:

\[
d = \sqrt{(4 - (-1))^2 + (9 - (-3))^2}
\]

This simplifies to:

\[
d = \sqrt{(4 + 1)^2 + (9 + 3)^2}
\]
\[
d = \sqrt{(5)^2 + (12)^2}
\]
\[
d = \sqrt{25 + 144}
\]
\[
d = \sqrt{169}
\]
\[
d = 13
\]

Thus, the length of the train's route from Walt City to Koshville is **13 miles**.