Distance story problem

Question

Did I solve this correctly?

 

Lily is at Buckingham Fountain, (5,-5) and wants to meet David, who is at Millennium Park, (2,1), for lunch.  They want to meet at the landmark that is closet to the midpint of their locations.  At which landmark should they meet?

(Arts Institute, (2, -2) or (Symphony Center (2,-3)

 

My answer is Arts Institute by solving it this way:

 

 1.   x1 + x2    +  y1  + y2       =              5  +  2      +   -5 + 1      =   7/2, -4/2  =  (3.5,-2)   (Midpoint for

     _________    ______                       _____            ______                                Buckingham to Millennium)

         2                    2                               2                    2

 

 2.  Arts Institute Distance  (2, -2)

 

      √(3.5 - 2)^2  + (-2- (-2))^2

 

  =    2.25 + 0 = 2.25 units

 

 

 3.  Symphony Center  (2,-3)

 

     √(3.5-2)^2 + (-2-(-3))^2

 

  =  2.25  + 1 = 3.25 units

 

 

 

Thanks!

 

 

 

 

 

Answer 1

You solved this correctly until the last part of step 2 and 3, but your answer is still correct. In step 2 you use the distance formula and set it up correctly but then you drop the √ sign in the last part. The distance would be the √2.25 which is 1.5. You make the same error in step 3 by forgetting to take the √ at the end. The distance for step 3 would be √3.25 or about 1.8. So yes the Art Institute is closer to the midpoint.