Find the Distance Between Two Points (-1/2,5/7) , (-8/3,1/21)

Math
(-12,57) , (-83,121)
Use the distance formula to determine the distance between the two points.
Distance=(x2-x1)2+(y2-y1)2
Substitute the actual values of the points into the distance formula.
((-83)-(-12))2+(121-57)2
Simplify.
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Multiply -(-12).
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Multiply -1 by -1.
(-83+1(12))2+(121-57)2
Multiply 12 by 1.
(-83+12)2+(121-57)2
(-83+12)2+(121-57)2
To write -83 as a fraction with a common denominator, multiply by 22.
(-83⋅22+12)2+(121-57)2
To write 12 as a fraction with a common denominator, multiply by 33.
(-83⋅22+12⋅33)2+(121-57)2
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
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Multiply 83 and 22.
(-8⋅23⋅2+12⋅33)2+(121-57)2
Multiply 3 by 2.
(-8⋅26+12⋅33)2+(121-57)2
Multiply 12 and 33.
(-8⋅26+32⋅3)2+(121-57)2
Multiply 2 by 3.
(-8⋅26+36)2+(121-57)2
(-8⋅26+36)2+(121-57)2
Combine the numerators over the common denominator.
(-8⋅2+36)2+(121-57)2
Simplify the numerator.
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Multiply -8 by 2.
(-16+36)2+(121-57)2
Add -16 and 3.
(-136)2+(121-57)2
(-136)2+(121-57)2
Move the negative in front of the fraction.
(-136)2+(121-57)2
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -136.
(-1)2(136)2+(121-57)2
Apply the product rule to 136.
(-1)213262+(121-57)2
(-1)213262+(121-57)2
Raise -1 to the power of 2.
113262+(121-57)2
Multiply 13262 by 1.
13262+(121-57)2
Raise 13 to the power of 2.
16962+(121-57)2
Raise 6 to the power of 2.
16936+(121-57)2
To write -57 as a fraction with a common denominator, multiply by 33.
16936+(121-57⋅33)2
Write each expression with a common denominator of 21, by multiplying each by an appropriate factor of 1.
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Multiply 57 and 33.
16936+(121-5⋅37⋅3)2
Multiply 7 by 3.
16936+(121-5⋅321)2
16936+(121-5⋅321)2
Combine the numerators over the common denominator.
16936+(1-5⋅321)2
Simplify the numerator.
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Multiply -5 by 3.
16936+(1-1521)2
Subtract 15 from 1.
16936+(-1421)2
16936+(-1421)2
Cancel the common factor of -14 and 21.
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Factor 7 out of -14.
16936+(7(-2)21)2
Cancel the common factors.
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Factor 7 out of 21.
16936+(7⋅-27⋅3)2
Cancel the common factor.
16936+(7⋅-27⋅3)2
Rewrite the expression.
16936+(-23)2
16936+(-23)2
16936+(-23)2
Move the negative in front of the fraction.
16936+(-23)2
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -23.
16936+(-1)2(23)2
Apply the product rule to 23.
16936+(-1)22232
16936+(-1)22232
Raise -1 to the power of 2.
16936+12232
Multiply 2232 by 1.
16936+2232
Raise 2 to the power of 2.
16936+432
Raise 3 to the power of 2.
16936+49
To write 49 as a fraction with a common denominator, multiply by 44.
16936+49⋅44
Write each expression with a common denominator of 36, by multiplying each by an appropriate factor of 1.
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Multiply 49 and 44.
16936+4⋅49⋅4
Multiply 9 by 4.
16936+4⋅436
16936+4⋅436
Combine the numerators over the common denominator.
169+4⋅436
Simplify the numerator.
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Multiply 4 by 4.
169+1636
Add 169 and 16.
18536
18536
Rewrite 18536 as 18536.
18536
Simplify the denominator.
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Rewrite 36 as 62.
18562
Pull terms out from under the radical, assuming positive real numbers.
1856
1856
1856
The result can be shown in multiple forms.
Exact Form:
1856
Decimal Form:
2.26691175…
Find the Distance Between Two Points (-1/2,5/7) , (-8/3,1/21)

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