What is the distance between #(4 ,( 7 pi)/6 )# and #(-1 ,( 3pi )/2 )#?

1 Answer
Anish M.
Mar 23, 2018

The distance between the two points is #sqrt(3)# units

Explanation:

To find the distance between these two points, first convert them into regular coordinates. Now, if #(r,x)# are the coordinates in polar form, then the coordinates in regular form are #(rcosx,rsinx)#.
Take the first point #(4,(7pi)/6)#.
This becomes #(4cos((7pi)/6),4sin((7pi)/6))#

=#(-2sqrt(3),-2)#

The second point is #(-1,(3pi)/2)#
This becomes #(-1cos((3pi)/2),-1sin((3pi)/2))#

=#(0,1)#

So now the two points are #(-2sqrt(3),-2)# and #(0,1)#. Now we can use the distance formula
#d=sqrt((-2sqrt(3)-0)^2 - (-2-1)^2)#

=#sqrt(12-9)#

=#sqrt(3)#

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