(37,-35) , (97,75)

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.

(97-37)2+(75-(-35))2

Subtract 37 from 97.

(67)2+(75-(-35))2

Simplify the expression.

Apply the product rule to 67.

6272+(75-(-35))2

Raise 6 to the power of 2.

3672+(75-(-35))2

3672+(75-(-35))2

Rewrite 72 as 7.

Use axn=axn to rewrite 7 as 712.

36(712)2+(75-(-35))2

Apply the power rule and multiply exponents, (am)n=amn.

36⋅712⋅2+(75-(-35))2

Combine 12 and 2.

36⋅722+(75-(-35))2

Cancel the common factor of 2.

Cancel the common factor.

36⋅722+(75-(-35))2

Divide 1 by 1.

36⋅71+(75-(-35))2

36⋅71+(75-(-35))2

Evaluate the exponent.

36⋅7+(75-(-35))2

36⋅7+(75-(-35))2

Multiply.

Multiply 36 by 7.

252+(75-(-35))2

Multiply -3 by -1.

252+(75+35)2

252+(75+35)2

Add 75 and 35.

252+(105)2

Simplify the expression.

Apply the product rule to 105.

252+10252

Raise 10 to the power of 2.

252+10052

252+10052

Rewrite 52 as 5.

Use axn=axn to rewrite 5 as 512.

252+100(512)2

Apply the power rule and multiply exponents, (am)n=amn.

252+100⋅512⋅2

Combine 12 and 2.

252+100⋅522

Cancel the common factor of 2.

Cancel the common factor.

252+100⋅522

Divide 1 by 1.

252+100⋅51

252+100⋅51

Evaluate the exponent.

252+100⋅5

252+100⋅5

Simplify the expression.

Multiply 100 by 5.

252+500

Add 252 and 500.

752

752

Rewrite 752 as 42⋅47.

Factor 16 out of 752.

16(47)

Rewrite 16 as 42.

42⋅47

42⋅47

Pull terms out from under the radical.

447

447

The result can be shown in multiple forms.

Exact Form:

447

Decimal Form:

27.42261840…

Find the Distance Between Two Points (3 square root of 7,-3 square root of 5) , (9 square root of 7,7 square root of 5)