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# Graph the points and answer:  If David wants to end his day at Navy Pier, would it be...

novjb | Salutatorian

Posted May 25, 2013 at 12:10 AM via web

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If David wants to end his day at Navy Pier, would it be more efficient to go to the Chicago Theater and then Millennium Park or to Millennium Park and then the the Chicago Theater?

Navy Pier is on point (10,9), The Chicago Theater is on point (0,3) and Millennium Park is on point (2,1).

I think I need to use the distance formula to find the distance between Navy Pier and the Chicago Theater,(which equals about 11.66 units), and the distance between Navy Pier and Millennium Park.(Which equals about 11.31). Because 11.66>11.31, David should go to Millennium Park and then to Chicago Theater.

Is this right?

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 25, 2013 at 2:38 AM (Answer #1)

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Let C be the point (0,3) (Chicago theater), M (2,1) (Millennium Park) , and N (10,9) (Navy Pier). We want the most efficient (i.e. shortest) route ending at N:

C->M->N `CM=sqrt((2-0)^2+(1-3)^2)=sqrt(4+4)=2sqrt(2)`

`MN=sqrt((10-2)^2+(9-1)^2)=sqrt(64+64)=8sqrt(2)`

Thus C->M->N has length `10sqrt(2)~~14.142`

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M->C->N `MC=2sqrt(2)` found above.

`CN=sqrt((10-0)^2+(9-3)^2)=sqrt(100+36)=2sqrt(34)`

Thus M->C->N has length `2sqrt(34)+2sqrt(2)~~14.49`

Since the route C->M->N is shorter, this is the more efficient route.

David should start at the Chicago Theater, go to Millennium Park, then to Navy Pier.

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