Answer:
[tex]4\sqrt{5}[/tex] miles.
Step-by-step 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:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, the distance between Elm and Symphony stations is
[tex]D=\sqrt{(1-(-3))^2+(2-(-6))^2}[/tex]
[tex]D=\sqrt{(1+3)^2+(2+6)^2}[/tex]
[tex]D=\sqrt{(4)^2+(8)^2}[/tex]
[tex]D=\sqrt{16+64}[/tex]
[tex]D=\sqrt{80}[/tex]
[tex]D=4\sqrt{5}[/tex]
Therefore, the distance between Elm and Symphony stations is [tex]4\sqrt{5}[/tex] miles.