Answer:
24.065 miles
Step-by-step explanation:
Antonio visited three cities on the coordinate grid at A(4, 5), B(-1, 3) and C(-3, -4), he visited the cities and ended up where he started. That means he moved from point A to B to C and back to A.
The distance (d) between two points (x₁, y₁) and (x₂, y₂) can be given as:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore distance between AB = [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-1-4)^2+(3-5)^2}=\sqrt{25+4}=5.385[/tex]
distance between BC = [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-3-(-1))^2+(-4-3)^2}=\sqrt{4+49}=7.28[/tex]
distance between CA = [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-(-3))^2+(5-(-4))^2}=\sqrt{49+81}=11.4[/tex]
The total distance = AB + BC + AC = 5.385 + 7.28 + 11.4 = 24.065 miles
