From the graph, angelica's house is represented by the point (4, 3) and the gas station is represented by the point (10, 8).
The distance between two given points in the xy-plane is given by
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
where:
[tex](x_1, y_1)=(4, 3) \ and \ (x_2, y_2)=(10, 8)[/tex]
Thus
[tex]d= \sqrt{(10-4)^2+(8-3)^2} \\ = \sqrt{6^2+5^2} = \sqrt{36+25} \\ = \sqrt{61} =7.81[/tex]
Therefore, the distance of the gas station from Angelica's house is 7.81 miles.
