What is the distance between $(2 , (5 pi)/4 )$ and $(8 , (3 pi )/2 )$ ?

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Answer 1 · 2018-06-24T07:16:52

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One way:

$(x,y) -> (rcostheta , rsintheta )$

$=> (2,(5pi)/4) =( 2cos ((5pi)/4 ) , 2sin( (5pi)/2) )$

$= (x_0 , y_0 ) = (-sqrt(2) , -sqrt(2) )$

$=> (8, (3pi)/2 )$ can be done the same way

$(x_1,y_1) = (0,-8 )$

Use Pythagorus' theorem

$d = sqrt((-sqrt(2) - 0 )^2 + ( -sqrt(2) - (-8) )^2 )$

$d = sqrt(68 +16sqrt(2) )$

This can be simplified further

What is the distance between (2 , (5 pi)/4 )(2 , (5 pi)/4 ) and (8 , (3 pi )/2 )(8 , (3 pi )/2 )?