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Alla [95]
3 years ago
11

Segment

ormula"> 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 $(a,b)$.
Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
7 0

Answer:

The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).

Step-by-step explanation:

Midpoint of a segment:

The coordinates of the midpoint of a segment are the mean of the coordinates of the endpoints of the segment.

Midpoint of s1:

Using the endpoints given in the exercise.

x = \frac{3 + \sqrt{2} + 4}{2} = \frac{7 + \sqrt{2}}{2}

y = \frac{5 + 7}{2} = \frac{12}{2} = 6

Thus:

M_{s1} = (\frac{7 + \sqrt{2}}{2},6)

Midpoint of s2:

x = \frac{6 - \sqrt{2} + 3}{2} = \frac{9 - \sqrt{2}}{2}

y = \frac{3 + 5}{2} = \frac{8}{2} = 4

Thus:

M_{s2} = (\frac{9 - \sqrt{2}}{2}, 4)

Find the midpoint of the segment with endpoints at the midpoints of s1 and s2.

Now the midpoint of the segment with endpoints M_{s1} and M_{s2}. So

x = \frac{\frac{7 + \sqrt{2}}{2} + \frac{9 - \sqrt{2}}{2}}{2} = \frac{16}{4} = 4

y = \frac{6 + 4}{2} = \frac{10}{2} = 5

The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).

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