# Find the Distance Between Two Points (1,- square root of 2) , (- square root of 13,0)

(1,-2) , (-13,0)
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.
((-13)-1)2+(0-(-2))2
Simplify.
Rewrite (-13-1)2 as (-13-1)(-13-1).
(-13-1)(-13-1)+(0-(-2))2
Expand (-13-1)(-13-1) using the FOIL Method.
Apply the distributive property.
-13(-13-1)-1(-13-1)+(0-(-2))2
Apply the distributive property.
-13(-13)-13⋅-1-1(-13-1)+(0-(-2))2
Apply the distributive property.
-13(-13)-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
-13(-13)-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Simplify and combine like terms.
Simplify each term.
Multiply -13(-13).
Multiply -1 by -1.
11313-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Multiply 13 by 1.
1313-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Raise 13 to the power of 1.
13113-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Raise 13 to the power of 1.
131131-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Use the power rule aman=am+n to combine exponents.
131+1-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
132-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
132-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Rewrite 132 as 13.
Use axn=axn to rewrite 13 as 1312.
(1312)2-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Apply the power rule and multiply exponents, (am)n=amn.
1312⋅2-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Combine 12 and 2.
1322-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Cancel the common factor of 2.
Cancel the common factor.
1322-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Divide 1 by 1.
131-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
131-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Evaluate the exponent.
13-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
13-13⋅-1-1(-13)-1⋅-1+(0-(-2))2
Multiply -13⋅-1.
Multiply -1 by -1.
13+113-1(-13)-1⋅-1+(0-(-2))2
Multiply 13 by 1.
13+13-1(-13)-1⋅-1+(0-(-2))2
13+13-1(-13)-1⋅-1+(0-(-2))2
Multiply -1(-13).
Multiply -1 by -1.
13+13+113-1⋅-1+(0-(-2))2
Multiply 13 by 1.
13+13+13-1⋅-1+(0-(-2))2
13+13+13-1⋅-1+(0-(-2))2
Multiply -1 by -1.
13+13+13+1+(0-(-2))2
13+13+13+1+(0-(-2))2
14+13+13+(0-(-2))2
14+213+(0-(-2))2
14+213+(0-(-2))2
Multiply -(-2).
Multiply -1 by -1.
14+213+(0+12)2
Multiply 2 by 1.
14+213+(0+2)2
14+213+(0+2)2
14+213+22
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
14+213+(212)2
Apply the power rule and multiply exponents, (am)n=amn.
14+213+212⋅2
Combine 12 and 2.
14+213+222
Cancel the common factor of 2.
Cancel the common factor.
14+213+222
Divide 1 by 1.
14+213+21
14+213+21
Evaluate the exponent.
14+213+2
14+213+2
16+213
16+213
The result can be shown in multiple forms.
Exact Form:
16+213
Decimal Form:
4.81779021…
Find the Distance Between Two Points (1,- square root of 2) , (- square root of 13,0)

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