Question

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?

Answer 1

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