Please use the grid but ignore the preprinted questions at b

Please use the grid, but ignore the pre-printed questions at bottom. Please answer the following question instead & show how to reach the conclusion mathematically.

1.) If Anthony 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 Chicago Theater?

Solve the following word problems. The grid below shows the approximate locations of some popular Chicago destinations as they relate to the center of the city (at State and Madison). Each has been labeled according to the chart at left. Use this grid to complete problems 22-24 on the next page; remember to show all your calculations using aerial distance Art Institute of Chicago Buckingham Fountain Chicago Theater Civic Opera House Chicago Cultural Center Daley Center (Picasso) Harold Washington Library Merchandise Mart Millennium Park Navy Pier Petrillo Music Shell Pritzker Pavilion Symphony Center Tribune Towers Willis (Sears) Tower C L 22. How far is the Merchandise Mart from Navy Pier, given that each unit is approximately mile? Round your answer to the nearest tenth of a mile. 23. Abby and Josh want to meet for dinner before Abby goes to a show at the Chicago Theater and Josh goes to a concert at Symphony Center They want to meet at the landmark that is closest to the midpoint of their after-dinner locations. At which landmark should they meet? 24. If Sophia wants to conclude her trip by seeing the Picasso at Daley Plaza, would it be more efficient to start her day at Millennium Park and then go to the opera or to see an opera and then go to Millennium Park?

Solution

coordinates of chicago centre(C) = (2,2)

coordinates of Nvay Pier (N) = ( 10, 9)

coordinates of Millenium park (K) =(2,1)

distance betweenC and N = sqrt(8^2 +7^2) = 10.63 units

distance between K and N = sqrt(8^2 +8^2) = 11.31 unit

Sice distnace between K and N is more than C and N so, it is more efficient to go

to first to Millenium park and then to Chicago theatre so that he travles less distnace there aftre from

chicgo theatre and Navy Pier

22. ) coordinates of Nvay Pier = ( 10, 9)

  coordinates of Merchandise mart = ( 5, 6)

Distance = sqrt( (10-5)^2 +(9-6)^2 ) = sqrt(25 +9) = 5.83 units

i unit = 1/8th mile

So, actual distance = 0.7 miles

24) coordinates of chicago theatre =( 0, 3)

coordinates of symphony theatre = (2 , -3)

midpoint = (2/2 , 0) = (1,0)

point closest to midpoint is K Milllenium park