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

(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.
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.
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.
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.
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.
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.
Multiply 289 by 9.
2601+676⋅436
Multiply 676 by 4.
2601+270436
530536
530536
Rewrite 530536 as 530536.
530536
Simplify the denominator.
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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