SOLUTION: The length of the line segment whose endpoints are (3,-2)and ( -4,5) is b square root 2 . What is the value of b

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Question 330311: The length of the line segment whose endpoints are (3,-2)and ( -4,5) is b square root 2 . What is the value of b
Found 2 solutions by nyc_function, jim_thompson5910:
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Use the distance formula for points.
b(sqrt[2]) = sqrt[(3 + 4)^2 + (-2 - 5)^2]
b(sqrt[2]) = sqrt[49 + 49]
b(sqrt[2]) = sqrt[98]
To find b, divide both sides by sqrt[2].
b = sqrt[98]/sqrt[2]
b = 7

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Note: is the first point . So this means that x%5B1%5D=3 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=-4 and y%5B2%5D=5.


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%283--4%29%5E2%2B%28-2-5%29%5E2%29 Plug in x%5B1%5D=3, x%5B2%5D=-4, y%5B1%5D=-2, and y%5B2%5D=5.


d=sqrt%28%287%29%5E2%2B%28-2-5%29%5E2%29 Subtract -4 from 3 to get 7.


d=sqrt%28%287%29%5E2%2B%28-7%29%5E2%29 Subtract 5 from -2 to get -7.


d=sqrt%2849%2B%28-7%29%5E2%29 Square 7 to get 49.


d=sqrt%2849%2B49%29 Square -7 to get 49.


d=sqrt%2898%29 Add 49 to 49 to get 98.


d=7%2Asqrt%282%29 Simplify the square root.


So our answer is d=7%2Asqrt%282%29


Since d=b%2Asqrt%282%29 and d=7%2Asqrt%282%29, this means that b%2Asqrt%282%29=7%2Asqrt%282%29


So b=7