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

Jan 30, 2016

4.468

#### Explanation:

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

suppose,
$A \left(4 , - 3 \frac{\pi}{4}\right)$

$B \left(- 2 , \frac{3 \pi}{4}\right)$

for A point

$x = 4 \cos \left(\frac{- 3 \pi}{4}\right) = - 2.828$

$y = 4 \sin \left(\frac{- 3 \pi}{4}\right) = - 2.828$

so, $A \left(- 2.828 , - 2.828\right)$

for B point,

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

$y = 2 \sin \left(\frac{3 \pi}{4}\right) = 1.41$

so, $B \left(- 1.41 , 1.41\right)$

so,

distance= $\sqrt{{\left(- 1.41 + 2.828\right)}^{2} + {\left(1.41 + 2.828\right)}^{2}} = \sqrt{19.97} = 4.468$