# Find the Distance Between Two Points (-1/2,5/7) , (-8/3,1/21) (-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.
Multiply -(-12).
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.
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.
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.
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.
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.
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.
Factor 7 out of -14.
16936+(7(-2)21)2
Cancel the common factors.
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.
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.
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.
Multiply 4 by 4.
169+1636
Add 169 and 16.
18536
18536
Rewrite 18536 as 18536.
18536
Simplify the denominator.
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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