What is the distance between #(4 ,( 7 pi)/8 )# and #(-1 ,( 3pi )/2 )#?

1 Answer
JMicheli
Jul 12, 2016

The distance is #(5sqrt(16 + pi^2))/4#

Explanation:

Distance between two points is the length of the vector between them. That is, for two points #vecA# and #vecB#, the distance will be: #||vecA - vecB||#.

This means that for your points:
#d = sqrt((4+1)^2 + ((7pi)/8 - (3pi)/2)^2)#
#= sqrt(5^2 + ((-5pi)/8)^2)#
#= sqrt(25 + (25pi^2)/16) = sqrt((400 + 25pi^2)/16)#
#= sqrt(400 + 25pi^2)/4 = (5sqrt(16 + pi^2))/4#

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