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).
+171 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) } $
