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Segment $s_1$ has endpoints at $(3+\sqrt{2},5)$ and $(4,7)$. Segment $s_2$ has endpoints at $(6-\sqrt{2},3)$ and $(3,5)$. Find the midpoint of the segment with endpoints at the midpoints of $s_1$ and $s_2$. Express your answer as $(a,b)$.

gueesstt  Apr 10, 2018
 #1
avatar+87714 
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\( (3+\sqrt{2},5)$ and $(4,7)\)

 

\( (6-\sqrt{2},3)$ and $(3,5)\)

 

 

Midpoint of the 1st segment  = ( [3 + √2 + 4']/2 , [7 + 5]/2 ) =  ( [7 + √2] / 2 , 6)

Midpoint of the second segment  = ( [ 6 - √2+ 3] / 2 , [5 + 3] / 2 ) =  ( [ 9 - √2] / 2 , 4 )

 

The midpoint of these two segments is  (  [ (7 + 9) / 2)/2 , [ 6 + 4 ]/ 2 )  =

(16/4, 10/2) = 

(  4,  5 )

 

 

cool cool cool

CPhill  Apr 10, 2018

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