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Margaret [11]
3 years ago
11

Antonio was visiting three cities that lie on a coordinate grid at A(4, 5), B(-1, 3) and C(-3, -4). If he visited the cities and

ended up where he started, how many miles did he travel?
Mathematics
1 answer:
Irina-Kira [14]3 years ago
7 0

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:

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

Therefore distance between AB = d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-1-4)^2+(3-5)^2}=\sqrt{25+4}=5.385

distance between BC = d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-3-(-1))^2+(-4-3)^2}=\sqrt{4+49}=7.28

distance between CA = d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-(-3))^2+(5-(-4))^2}=\sqrt{49+81}=11.4

The total distance = AB + BC + AC = 5.385 + 7.28 + 11.4 = 24.065 miles

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