Point A is at #(-2 ,9 )# and point B is at #(-1 ,4 )#. 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?

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Answer 1 · 2018-02-07T03:29:54

New coordinates of #color(red)(A' ((-9),(-2))#

Change in distance between A & B is #color(blue)(+4.9)#

Point A (-2,9), B (-1,4). Point A Rotated about origin by #(3pi)/2# clockwise.

That means A moves from II quadrant to III quadrant.

Distance #vec(AB) = sqrt((-2+1)^2 + (9-4)^2) = sqrt26 ~~ color(red)(5.1)#

#A ((-2),(9)) to A' ((-9),(-2))#

Distance #vec(A'B) = sqrt((-9+1)^2 + (-2-4)^2) = color(red)(10#

Change in distance #=color(blue)(10 - 5.1 = +4.9)#