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Segment s1 has endpoints at \((3+\sqrt{2},5) \)and (4,7). Segment s2 has endpoints at \((6-\sqrt{2},3)\) and (3,5). Find the midpoint of the segment with endpoints at the midpoints of s1 and s2. Express your answer as (a,b).

 Jun 27, 2021
 #1
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use $ (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})   $

for $(3+\sqrt{2},5)$ and $(4, 7)$ :

$( \frac{3+\sqrt{2}+4}{2}, \frac{5+7}{2})  $

$D_{s1}=( 4.2, 6)  $


for the 2nd one $  (6-\sqrt{2},3)$ and $(3, \: 5)$

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

$ D_{s2}=(3.8,\: 4 )  $

so the coordinates of the midline are $ ( 4.2, 6) $ and $ (3.8,\: 4 ) $

again doing the same thing:

$ ( \frac{4.2+3.8}{2}, \frac{6+4}{2} )  $

$ \boxed{D_{s3(midline)}=(4,\: 5) } $
 

 Jun 27, 2021

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