Find the Distance Between Two Points (13/2,4/3) , (-2,10)

Math
(132,43) , (-2,10)
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.
((-2)-132)2+(10-43)2
Simplify.
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To write -2 as a fraction with a common denominator, multiply by 22.
(-2⋅22-132)2+(10-43)2
Combine -2 and 22.
(-2⋅22-132)2+(10-43)2
Combine the numerators over the common denominator.
(-2⋅2-132)2+(10-43)2
Simplify the numerator.
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Multiply -2 by 2.
(-4-132)2+(10-43)2
Subtract 13 from -4.
(-172)2+(10-43)2
(-172)2+(10-43)2
Move the negative in front of the fraction.
(-172)2+(10-43)2
Use the power rule (ab)n=anbn to distribute the exponent.
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Apply the product rule to -172.
(-1)2(172)2+(10-43)2
Apply the product rule to 172.
(-1)217222+(10-43)2
(-1)217222+(10-43)2
Raise -1 to the power of 2.
117222+(10-43)2
Multiply 17222 by 1.
17222+(10-43)2
Raise 17 to the power of 2.
28922+(10-43)2
Raise 2 to the power of 2.
2894+(10-43)2
To write 10 as a fraction with a common denominator, multiply by 33.
2894+(10⋅33-43)2
Combine 10 and 33.
2894+(10⋅33-43)2
Combine the numerators over the common denominator.
2894+(10⋅3-43)2
Simplify the numerator.
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Multiply 10 by 3.
2894+(30-43)2
Subtract 4 from 30.
2894+(263)2
2894+(263)2
Apply the product rule to 263.
2894+26232
Raise 26 to the power of 2.
2894+67632
Raise 3 to the power of 2.
2894+6769
To write 2894 as a fraction with a common denominator, multiply by 99.
2894⋅99+6769
To write 6769 as a fraction with a common denominator, multiply by 44.
2894⋅99+6769⋅44
Write each expression with a common denominator of 36, by multiplying each by an appropriate factor of 1.
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Multiply 2894 and 99.
289⋅94⋅9+6769⋅44
Multiply 4 by 9.
289⋅936+6769⋅44
Multiply 6769 and 44.
289⋅936+676⋅49⋅4
Multiply 9 by 4.
289⋅936+676⋅436
289⋅936+676⋅436
Combine the numerators over the common denominator.
289⋅9+676⋅436
Simplify the numerator.
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Multiply 289 by 9.
2601+676⋅436
Multiply 676 by 4.
2601+270436
Add 2601 and 2704.
530536
530536
Rewrite 530536 as 530536.
530536
Simplify the denominator.
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Rewrite 36 as 62.
530562
Pull terms out from under the radical, assuming positive real numbers.
53056
53056
53056
The result can be shown in multiple forms.
Exact Form:
53056
Decimal Form:
12.13923848…
Find the Distance Between Two Points (13/2,4/3) , (-2,10)

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