Help solving distance problem

Question

 

If Anthony wants to end his day at Navy Pier, (10,9), would it be more efficient to go the Chicago Theater, (0,3) and then Millinnium Park (2,1) or to Millinnium Park (2,1) and then to Chicago Theater (0,3).

 

 

thanks

Answer 1

Alright. Distance formula
D = √((x₁ - x₂)² + (y₁ - y₂)²)

 

We have three distances that we are dealing with. Between the Theater and the Park, between the Theater and the Pier, and between the Park and the pier.

 

In both routes we have to go between the Theater and the Park. The distance between those is the same regardless of which way we go, so we can ignore doing the math for that.

 

That leaves us two distances. Let's plug them in.

 

Theater to Pier

D = √((0 - 10)² + (3 - 9)²) = √(100 + 36) ≈ 11.6619

 

Park to Pier

D = √((2 - 10)² + (1 - 9)²) = √(64 + 64) ≈ 11.3137

 

11.3 < 11.7

 

so starting at the theater is the fastest route.