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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),8) and (3,15). Find the midpoint of the segment with endpoints at the midpoints of s_1 and s_2. Express your answer as (a,b).

 Nov 15, 2020
 #1
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Midpoint of S1  =   [  (3 + sqrt (2) + 4)/2  , ( 5 + 7)/2 ]  =  [ (7 + sqrt (2)) / 2  , 6  ]

 

Midpoint of S2  =   [ ( 6 - sqrt (2) + 3 ) / 2  , (8 + 15) / 2  ]  =  [ (9-sqrt (2)) / 2, 23/2 ]

 

 Midpoint of the segment with endpoints at the midpoints of s_1 and s_2

 

[ (7 + sqrt (2) + 9 - sqrt (2) ) / 2  ,  ( 6 + 23/2) / 2 ]  =

 

[ 16/2 ,  (12/2 + 23/2) / 2 ]  =

 

( 8 , 35 / 4 )

 

 

cool cool cool

 Nov 15, 2020

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