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

24.065 miles

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=√((x_2-x_1)^2+(y_2-y_1)^2)`

Therefore distance between AB =
`d=√((x_2-x_1)^2+(y_2-y_1)^2)=√((-1-4)^2+(3-5)^2)=√(25+4)=5.385`

distance between BC =
`d=√((x_2-x_1)^2+(y_2-y_1)^2)=√((-3-(-1))^2+(-4-3)^2)=√(4+49)=7.28`

distance between CA =
`d=√((x_2-x_1)^2+(y_2-y_1)^2)=√((4-(-3))^2+(5-(-4))^2)=√(49+81)=11.4`

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