What is the distance between #(4 ,( - 3pi)/4 )# and #(7 ,( 3 pi )/4 )#?

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Answer 1 · 2016-02-26T14:41:33

#8.06#

Point #(4,−(3pi)/4)# in Cartesian coordinates represents #(4cos(−(3pi)/4)), 4sin(−(3pi)/4))#

i.e. #(4xx((-1)/sqrt2), 4xx((-1)/sqrt2))# or #(-4/sqrt2, -4/sqrt2)# or
#(-2sqrt2,-2sqrt2)#

Point #(7,(3pi)/4)# in Cartesian coordinates represents #(7cos(3pi/4)),7sin(3pi/4)))#

i.e. #(7xx((-1)/sqrt2), 7xx((1)/sqrt2))# or #(-7/sqrt2, 7/sqrt2)# or
#(-3.5sqrt2, 3.5sqrt2)#

Hence distance between #(-3.5sqrt2, 3.5sqrt2)# and #(-2sqrt2,-2sqrt2)#

is #sqrt((-2sqrt2+3.5sqrt2)^2+(-2sqrt2-3.5sqrt2)^2#

= #sqrt((1.5sqrt2)^2+(-5.5sqrt2)^2#

= #sqrt(2.25xx2+30.25xx2)#

= #sqrt(4.5+60.5)# = #sqrt65)= 8.06#