SOLUTION: what is the circumference of the circle that has a center at (1,1) and passes through point (3,5)

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Question 857145: what is the circumference of the circle that has a center at (1,1) and passes through point (3,5)
Found 2 solutions by reviewermath, jim_thompson5910:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
What is the circumference of the circle that has a center at (1,1) and passes through point (3,5)
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A:
The distance between (1, 1) and (3, 5) is equal to
sqrt%28%285+-+1%29%5E2+%2B+%283+-+1%29%5E2%29 = sqrt%2820%29 = 2sqrt%285%29.
The length of the radius is 2sqrt%285%29, so the circumference of the circle is equal to 2%2Api%2Ar = 2%2Api%2A2sqrt%285%29 = highlight%284pi%2Asqrt%285%29%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First we need the distance from (1,1) to (3,5)

Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (1, 1), we can say (x1, y1) = (1, 1)
So x%5B1%5D+=+1, y%5B1%5D+=+1


Since the second point is (3, 5), we can also say (x2, y2) = (3, 5)
So x%5B2%5D+=+3, y%5B2%5D+=+5


Put this all together to get: x%5B1%5D+=+1, y%5B1%5D+=+1, x%5B2%5D+=+3, and y%5B2%5D+=+5

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Now use the distance formula to find the distance between the two points (1, 1) and (3, 5)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%281+-+3%29%5E2+%2B+%281+-+5%29%5E2%29 Plug in x%5B1%5D+=+1, y%5B1%5D+=+1, x%5B2%5D+=+3, and y%5B2%5D+=+5


d+=+sqrt%28%28-2%29%5E2+%2B+%28-4%29%5E2%29


d+=+sqrt%284+%2B+16%29


d+=+sqrt%2820%29


d+=+sqrt%284%2A5%29


d+=+sqrt%284%29%2Asqrt%285%29


d+=+2%2Asqrt%285%29


d+=+4.47213595499958

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Answer:


The distance between the two points (1, 1) and (3, 5) is exactly 2%2Asqrt%285%29 units


The approximate distance between the two points is about 4.47213595499958 units



So again,


Exact Distance: 2%2Asqrt%285%29 units


Approximate Distance: 4.47213595499958 units





So the distance from (1,1) to (3,5) is exactly 2%2Asqrt%285%29 units

This makes the radius to be r+=+2%2Asqrt%285%29


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Now use this radius to find the circumference


C+=+2%2Api%2Ar


C+=+2%2Api%2A2%2Asqrt%285%29


C+=+2%2A2%2Api%2Asqrt%285%29


C+=+4%2Api%2Asqrt%285%29 This is the exact circumference in terms of pi


C+=+28.0992589242 Use a calculator to get the approximate circumference