Point A is at #(-6 ,1 )# and point B is at #(2 ,8 )#. 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
Jul 31, 2018

#color(green)("Change in dist. due to the rotation" = sqrt113 - sqrt65 ~~ 1.3185

Explanation:

https://www.onlinemath4all.com/algebraic-representations-of-rotations.html

#A (-6, 1), B (2, 8), " rotated about origin by " (3pi)/2 " clockwise"#

#A (-6, 1) to A' (-1, -6)#

#B ( 2, 8) to B' (-8, 2)#

#"Distance " bar(AB) = sqrt ((-6 - 2)^2 + (1 - 2)^2) = sqrt 65#

#"Distance " bar(A'B') = sqrt ((-1 - -8)^2 + (-6 - 2)^2) = sqrt 113#

#color(green)("Change in dist. due to the rotation" = sqrt113 - sqrt65 ~~ 1.3185#

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