Point A is at #(-5 ,-1 )# and point B is at #(-5 ,-3 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

1 Answer
sankarankalyanam
Feb 22, 2018

Increase in distance due to rotation of A is #color(blue)(d = 4.3246#

Explanation:

http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0256-01002012000100003

#A (-5,-1), B(-5,-3)# A Rotated about origin by #(3pi)/2# clockwise.

#vec(AB) = sqrt ((-5+5)^2 + (-1+3)^2) = 2#

#A ((-5),(-1)) -> A’((1),(-5))#

#vec(A’B) = sqrt ((1+5)^2 + (-5+3)^2) = 6.3246#

Increase in distance due to rotation of A is

#color(blue)(d = 6.3246 - 2 = 4.3246#

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