Question

Find the distance between the points (2,1) and (1,-1/3)

Answer 1

`\boxed{d = (5)/(3)}`

Explanation:

`given \: points \: (2,1) \: and \: (1, - (1)/(3)): \\ d \: = \sqrt{ (x _(2) - x_(1))^(2) +(y_(2) - y_(1))^(2) } \\ d \: = \sqrt{ (1 - 2)^(2) +( - (1)/(3) - 1)^(2) } \\ d \: = \sqrt{ ( - 1)^(2) +( - (4)/(3))^(2) } \\d \: = \sqrt{ (1) +( (16)/(9)) } \\d \: = \sqrt{ 1 + (16)/(9) } \\d \: = \sqrt{ (9)/(9) + (16)/(9) } \\d \: = \sqrt{ (25)/(9) }\\d \: = (√( 25 ))/(√( 9 )) \\d \: = ( 5)/(3)`