What is the distance between #(4 ,(5 pi)/6 )# and #(-1 , (19 pi )/12 )#?

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Answer 1 · 2018-06-30T21:47:06

#~~10.55# units

We want to use the Distance Formula, which is really derived from the Pythagorean theorem.

Distance Formula

#sqrt((Deltax)^2+(Deltay)^2)#

Where #Delta# is the Greek letter denoting "change in".

How much does our #x# change by?

Well we go from #4# to #-1#, so this means

#color(blue)(Deltax=-5)#

How much does our #y# change by?

#y# starts out at #(10pi)/12#, but goes to #(19pi)/12#. We can say

#Deltay=(9pi)/12# or #color(blue)(Deltay=(3pi)/4)#

Let's plug these into the distance formula to get

#sqrt((-5)^2+((3pi)/4)^2)#

This simplifies to

#5+9/16 pi^2#

Which is approximately

#5+5.55=10.55# units

Hope this helps!