Point A is at #(-6 ,1 )# and point B is at #(3 ,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?

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Answer 1 · 2017-06-24T07:20:29

The new coordinates are #=(-1,-6)# and the distance has changed by #=3.2#

The matrix of a rotation clockwise by #3/2pi# about the origin is

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

Therefore, the transformation of point #A# is

#A'= ((0,-1),(1,0)) ((-6),(1))=((-1),(-6))#

The distance #AB# is

#=sqrt((3-(-6))^2+(8-1)^2)#

#=sqrt(81+49)#

#=sqrt130#

The distance #A'B# is

#=sqrt((3-(-1))^2+(8-(-6))^2)#

#=sqrt(16+196)#

#=sqrt212#

The distance has changed by

#=sqrt212-sqrt130#

#=3.2#