Question

The units of the subway map at the right are in miles. Suppose the routes between stations are straight, find the distance you would travel between each the Elm and Symphony Stations. Round your answer to the nearest tenth of a mile.

Answer 1

The distance between the Elm and Symphony Stations is equal to 8.9 miles.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance =
`√((x_2-x_1)^2 + (y_2-y_1)^2)`

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Based on the graph, we can logically deduce the following end points for both Elm and Symphony Stations;

• Elm = (-3, -6)
• Symphony Stations = (1, 2)

By substituting the given end points (-3, -6) and (1, 2) into the distance formula, we have the following;

`Distance = √((x_2-x_1)^2 + (y_2-y_1)^2)\\\\Distance = √((1-(-3))^2 + (2-(-6))^2)\\\\Distance = √((1+ 3)^2 + (2+6)^2)\\\\Distance = √((4)^2 + (8)^2)\\\\Distance = √(16 + 64)\\\\Distance = √(80)`

Distance = 8.944 ≈ 8.9 miles.

Answer 2

`4√(5)` miles.

Explanation:

From the given figure it is clear that the coordinates of Elm station are (-3,-6) and coordinates of Symphony station are (1,2).

Distance formula:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula, the distance between Elm and Symphony stations is

`D=√((1-(-3))^2+(2-(-6))^2)`

`D=√((1+3)^2+(2+6)^2)`

`D=√((4)^2+(8)^2)`

`D=√(16+64)`

`D=√(80)`

`D=4√(5)`

Therefore, the distance between Elm and Symphony stations is
`4√(5)` miles.