SOLUTION: Compute the distance between the two points (1-√2,-1) and (2+√2,4).

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Question 980913: Compute the distance between the two points (1-√2,-1) and (2+√2,4).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Distance Formula


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


Since the first point is (-0.414213562373095, -1), we can say (x1, y1) = (-0.414213562373095, -1)
So x%5B1%5D+=+-0.414213562373095, y%5B1%5D+=+-1


Since the second point is (3.41421356237309, 4), we can also say (x2, y2) = (3.41421356237309, 4)
So x%5B2%5D+=+3.41421356237309, y%5B2%5D+=+4


Put this all together to get: x%5B1%5D+=+-0.414213562373095, y%5B1%5D+=+-1, x%5B2%5D+=+3.41421356237309, and y%5B2%5D+=+4

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Now use the distance formula to find the distance between the two points (-0.414213562373095, -1) and (3.41421356237309, 4)



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


d+=+sqrt%28%28-0.414213562373095+-+3.41421356237309%29%5E2+%2B+%28-1+-+4%29%5E2%29 Plug in x%5B1%5D+=+-0.414213562373095, y%5B1%5D+=+-1, x%5B2%5D+=+3.41421356237309, and y%5B2%5D+=+4


d+=+sqrt%28%28-3.82842712474618%29%5E2+%2B+%28-5%29%5E2%29


d+=+sqrt%2814.6568542494923+%2B+25%29


d+=+sqrt%2839.6568542494923%29


d+=+6.29736883543376

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Answer:


The distance between the two points (-0.414213562373095, -1) and (3.41421356237309, 4) is exactly sqrt%2839.6568542494923%29 units


The approximate distance between the two points is about 6.29736883543376 units



So again,


Exact Distance: sqrt%2839.6568542494923%29 units


Approximate Distance: 6.29736883543376 units