What is the distance between $(3 ,( pi)/12 )$ and $(-4 , ( 3 pi )/2 )$ ?

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Answer 1 · 2017-11-13T22:05:12

$4.33color(white)(88)$ units

First we need to convert the polar coordinates to Cartesian coordinates. We can do this by using the following:

$x =rcos(theta)$

$y=rsin(theta)$

$:.$

$x=3cos(pi/12)=2.90$

$y=3sin(pi/12)=0.78$

Cartesian coordinate:

$( 2.9 , 0.78 )$

$x=-4cos((3pi)/2)=0$

$y=-4sin((3pi)/2)=4$

Cartesian coordinate:

$( 0 , 4 )$

Next we use the distance formula:

$d = sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

$d=sqrt((2.9-0)^2+(0.78-4)^2)=4.33color(white)(88)$ units

All results to 2 .d.p.

What is the distance between (3 ,( pi)/12 )(3 ,( pi)/12 ) and (-4 , ( 3 pi )/2 )(-4 , ( 3 pi )/2 )?