What is the distance between $(4, \frac{- 3 π}{4})$ $(4 ,( - 3pi)/4 )$ and $(2, \frac{3 π}{4})$ $(2 ,( 3 pi )/4 )$ ?

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Answer 1 · 2016-01-30T13:30:36

4.468

at first, we have to transform the two points into Cartesian form.
so,

suppose,
$A (4, - 3 \frac{π}{4})$ $A(4,-3pi/4)$

$B (- 2, \frac{3 π}{4})$ $B(-2,(3pi)/4)$

for A point

$x = 4 cos (\frac{- 3 π}{4}) = - 2.828$ $x=4cos((-3pi)/4)=-2.828$

$y = 4 sin (\frac{- 3 π}{4}) = - 2.828$ $y=4sin((-3pi)/4)=-2.828$

so, $A (- 2.828, - 2.828)$ $A(-2.828,-2.828)$

for B point,

$x = 2 cos (\frac{3 π}{4}) = - 1.41$ $x=2cos((3pi)/4)=-1.41$

$y = 2 sin (\frac{3 π}{4}) = 1.41$ $y=2sin((3pi)/4)=1.41$

so, $B (- 1.41, 1.41)$ $B(-1.41,1.41)$

so,

distance= $\sqrt{{(- 1.41 + 2.828)}^{2} + {(1.41 + 2.828)}^{2}} = \sqrt{19.97} = 4.468$ $sqrt((-1.41+2.828)^2+(1.41+2.828)^2)=sqrt19.97=4.468$

What is the distance between (4,−3π4)(4 ,( - 3pi)/4 ) and (2,3π4)(2 ,( 3 pi )/4 )?