Minimizing the sum of two distances, Mathematics

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The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

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Lora 3/29/2013 3:46:31 AM the minimum distance of the points from (1,y) is the distance from the intersection of their perpendicular bisectors to the line x=1 hence slope of perpendicular bisector=> -4=2y-14 / 2x -7 => 8x + 2y = 42. putting x=1,y=17, hence a+b= 17 +1 =18 (ANS).

Lora

3/29/2013 3:46:31 AM

the minimum distance of the points from (1,y) is the distance from the intersection of their perpendicular bisectors to the line x=1
hence slope of perpendicular bisector=> -4=2y-14 / 2x -7
=> 8x + 2y = 42.
putting x=1,y=17,
hence a+b= 17 +1 =18 (ANS).

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