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 $sqrt((-2sqrt2+3.5sqrt2)^2+(-2sqrt2-3.5sqrt2)^2$

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

= $sqrt(2.25xx2+30.25xx2)$

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

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