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