Point A is at #(9 ,3 )# and point B is at #(1 ,-6 )#. Point A is rotated #pi/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 · 2017-06-28T07:18:12

The new coordinates are #=(3,-9)# and the distance has changed by #=8.4#

The matrix of a rotation clockwise by #1/2pi# about the origin is

#((0,1),(-1,0))#

Therefore, the transformation of point #A# is

#A'= ((0,1),(-1,0)) ((9),(3))=((3),(-9))#

The distance #AB# is

#=sqrt((1-(9))^2+(-6-3)^2)#

#=sqrt(64+81)#

#=sqrt145#

The distance #A'B# is

#=sqrt((1-(3))^2+(-6-(-9))^2)#

#=sqrt(4+9)#

#=sqrt13#

The distance has changed by

#=sqrt145-sqrt13#

#=8.4#